The value of x for which the rational expression equals to zero is -4
What is System of Linear Equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.
The equation is
2 - x +x/2 + x = 0
⇒ x/2 = -2
⇒ x = -4
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Determine if the scenario involves mutually exclusive events.
A box of chocolates contains five milk chocolates, five dark chocolates, and three
white chocolates. You randomly select a chocolate. It is a milk chocolate or a dark chocolate.
A) Not mutually exclusive
B) Mutually exclusive
The given question where we randomly select a chocolate. It is a milk chocolate or dark chocolate is a mutually exclusive chocolate
How do you calculate probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. Probability is a measure of how likely something is to occur. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur.
In the given question
we see
Selecting a milk chocolate or dark chocolate is mutually exclusive event as they are not related to each other
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A quantity with an initial value of 4400 grows continuously at a rate of 0.5% per year. What is the value of the quantity after 46 years, to the nearest hundredth?
Answer:
To find the value of the quantity after 46 years, we can use the formula for continuous compound interest:
A = P(1 + r)^t
Where:
A = final amount
P = initial amount (4400)
r = rate of growth (0.5%)
t = number of years (46)
We need to convert the percentage rate to decimal form, so we divide the rate by 100
0.5/100 = 0.005
Now we can substitute the values into the formula:
A = 4400(1 + 0.005)^46
A = 4400(1.005)^46
A = 4400 * 1.294624
A = 5685.89
Therefore, the value of the quantity after 46 years is 5685.89, to the nearest hundredth.
Step-by-step explanation:
Zahara rides with her to her grandmother's house. They travel 159 miles in 3 hours. Her uncle Jorge drives there separately from his home.
a. At what speed does Zahara's dad drive in miles per hour
b. Jorge's trip takes the same time as Zahara's, but he travels a shorter distance. Does Jorge drive faster or slower than Zahara's dada
Answer: a. To find the speed at which Zahara's dad drives, we need to divide the distance traveled by the time it took to travel that distance. The formula is: speed = distance/time.
So, speed = 159 miles / 3 hours = 53 miles per hour
b. Since Zahara's trip and Jorge's trip took the same amount of time, the only way that Jorge could have traveled a shorter distance than Zahara is if he drove slower. So, it can be inferred that Jorge drives slower than Zahara's dad.
Step-by-step explanation:
Solve for z.
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The value of the z is 6√6 units. The triangles follow similar triangle property.
What are similar triangles?
Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.
Consider △BDC and △ABC:
∠C = ∠C
∠ABC = ∠BDC = right angle
If two angles of a triangle are equal to two angles of another triangle, then third angle of the triangles also equal.
∠BAC =∠DBC
According to A-A-A rule △BDC and △ABC are similar to each other.
Thus the ratio of corresponding sides is also equal.
Therefore:
AB/BD = BC/DC = AC/ BC
Consider the last two ratios:
BC/DC = AC/ BC
z/12 = z/18
z² = 12 × 18
z² = 6×2×6×3
z = 6√6
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A shopper at a clearance sale is pleased to discover some bottles of hand lotion on sale for $2.49 each. The original price tags read $3.25. What is the discount percentage?
Round your answer to the nearest percent and include a percent sign
HELPPPPP PLEASE
Answer: The discount percentage is 23.4%
Step-by-step explanation:
The discount percentage can be calculated by taking the difference between the original price and the sale price, dividing that by the original price, and then multiplying by 100 to get a percentage.
Prove that if parallel lines are crossed by a transversal, then the alternate interior angles are congruent. That is, use rigid transformations to map ∠CFG onto ∠BCF. Explain.
Alternate interior angles are congruent if parallel lines are crossed by a transversal.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
A figure has been shown below,
Where there is 2 parallel line intersected by a transversal line.
The measure of the alternate angle [besides interior and exterior angle], their measure are equal to corresponding angles as well as with alternate angles. As shown in the figure.
Thus, alternate interior angles are congruent if parallel lines are crossed by a transversal.
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Jean joined a gym. It costs $60 per month and $2 per hour of boxing classes. Write an expression to represent the total cost of his gym, including the boxing classes for a month. Then determine how much it would cost him, if he spent 19.5 hours in gym class that month.
Answer:
y= 60+ 2x and if he spent 19.5 hours then he would pay $99 for that month
Step-by-step explanation:
$60 PER MONTH + $2 per hour of boxing classes
X represents the total hours he had the boxing classes
equation: y= 60+ 2x
if he spent 19.5 hours in boxing class
plug in 19.5 hours to X
99 = 60+ 2(19.5) = 60 + 39
use the triangle sum theorem to find 7x + 4x + x = 180
Answer: x = 15
Step-by-step explanation: Combine like terms
7 x plus 4 x plus x equals 180
12 x equals 180
2
Divide both sides by the same factor
12 x equals 180
the fraction with numerator 12 x and denominator 12 end fraction equals the fraction with numerator 180 and denominator 12 end fraction
3
Simplify
Solution
x equals 15
find the sum of the series. [infinity] (−1)n 8nx6n n! n = 0
Sum of the series will be (19/30)
Partial differentiation is the method of determining a function's partial derivative. By holding the other variable constant, one may use this method to get the partial derivative of a function with respect to one variable.
An equation having an unknown function of two or more variables and its partial derivatives with respect to these variables is known as a partial differential equation. A partial differential equation has the highest-order derivatives as its order. is a partial differential equation of order 2, as an illustration.
Ordinary differential equations, often known as ODEs, are equations for which only one variable's derivatives are considered. Consequently, there is just one independent variable. PDEs are equations that rely on the partial derivatives of a number of distinct variables.
Using partial fractions, we have
[tex]\frac{6}{(n+8)(n+10)}=\frac{A}{n+8}+\frac{B}{n+10}\\\\=\frac{A(n+10)+B(n+8)}{(n+8)(n+10)} \\\\ 6=A(n+8)+B(n+10)[/tex]
Put n=-8,
we have 6=0+2B=>B=3
Put n=-10,
we have 6=-2A =>A=-3
[tex]$$\begin{aligned}& \sum_{n=1}^{\infty} \frac{6}{(n+8)(n+10)}=\sum_{n=1}^{\infty}\left(\frac{3}{n+8}-\frac{3}{n+10}\right) \\& =3 \sum_{n=1}^{\infty} \frac{1}{n+8}-\frac{1}{n+10} \\& =3\left[\left(\frac{1}{9}-\frac{1}{11}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{11}-\frac{1}{13}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)+\ldots\right] \\& =3\left[\frac{1}{9}+\frac{1}{10}\right]=\frac{19}{30}\end{aligned}$$[/tex]
other terms will be cancelled out
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The correct question should be:
Find the sum of the convergent series: [tex]$$\sum_{n=1}^{\infty} 6 /(n+8)(n+10)$$[/tex]
A car is purchased for $22,500. After each year, the resale value decreases by 30%. What will the resale value be after 4 years?
Use the calculator provided and round your answer to the nearest dollar.
On solving the provided question, exponents, resale value be $5339 after 4 years.
Exponents in math: what are they?The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) means 2 x 2 x 2 = 8. and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
y = cn^x
y is the new price, c is the starting price, n is the rate of increase (or decrease), and x is the number of years. I won't bore you with the various names this exponent use has in calculus and economics.
In our instance:
By calculating how much of the price will remain, we can determine n.
1.00 — 0.25 = 0.75
f(x) = (22500)(0.75)^x
f(5) = (22500)(0.75)^5
=5339.35
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Pedro has a tax-free savings account (TFSA) with a balance of
$2350.00. His interest is earned at a rate of 2.10%, compounded monthly. If he
contributes $400.00 to the TFSA at the end of every month, how long will it take
him to save $15 000.00?
You can hold qualified investments like cash, stocks, bonds, mutual funds in a TFSA and can withdraw contributions as well as the interest, capital gains, and dividends earned in the account at any time1, without paying taxes
What is the use of TFSA?Any individual that is a non-resident of Canada who has a valid SIN and who is 18 years of age or older is also eligible to open a TFSA. However, any contributions made while a non-resident will be subject to a 1% tax for each month the contribution stays in the account.A TFSA allows you to set money aside in eligible investments and watch those savings grow tax-free throughout your lifetime. Interest, dividends, and capital gains earned in a TFSA are tax-free for life.The single biggest benefit of a TFSA is that growth of all assets within it are tax-free: this includes interest, dividends and capital gains. You won't pay a penny in income tax even when you withdraw from your account or sell the assets inside the TFSATo know more about tax visit:
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Find the limit as (x,y) approach (0,0) pf the function (cos(xy) -1)/(x^2y^2)
The limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined.
We can see that the denominator [tex]x^2[/tex][tex]y^2[/tex] goes to 0 as (x,y) approaches (0,0), and that can cause the function to go to infinity. However, the numerator (cos(xy) -1) does not have a specific value as (x,y) approaches (0,0) the cosine function oscillates between -1 and 1 as xy approaches zero, and therefore it does not approach a specific value.
The term (x,y) → (0,0) means that x and y are approaching 0 independently. There are different paths in which x and y can approach zero. Hence, by the squeeze theorem, we can see that if we approach (x,y) to (0,0) along the path y = mx, where m is a nonzero constant, the function goes to infinity, but if we approach (x,y) to (0,0) along the path x = 0 or y = 0, the function goes to -1.
Therefore, the limit of the function (cos(xy) -1)/([tex]x^2[/tex][tex]y^2[/tex]) as (x,y) approaches (0,0) is not defined, as the function does not approach a specific value along all paths.
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Find the following cardinalities:
a. A when A= {5, 6, 7, 8, ..., 35}.
b. A when A= {xEZ: -2 ≤ x ≤ 90}.
c. An B| when A= {x EN: x ≤ 31} and B = {x EN: x is prime}
Therefore , the solution of the given problem of set A when A= {5, 6, 7, 8, ..., 35}.
What does the math set mean?In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.
Here,
The set A contains integers between 5 and 35, inclusive. So, the cardinality of set A is the number of integers between 5 and 35, which is 35-5+1 = 31.
b. A when A= {xEZ: -2 ≤ x ≤ 90}.
The set A contains all integers between -2 and 90, inclusive. So, the cardinality of set A is the number of integers between -2 and 90, which is 90-(-2)+1 = 93.
c. An B| when A= {x EN: x ≤ 31} and B = {x EN: x is prime}
The set A contains all the natural numbers less than or equal to 31. The set B contains all the prime numbers less than or equal to 31. There are 15 prime numbers less than or equal to 31: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. So, the cardinality of set B is 15.
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Situation #6
=
It is known that ΔTOP~ΔBUG. Also, TO = 16, TP = 20, OP = 30, and BG = 105.
6. What is the perimeter of ΔBUG?
The perimeter of Δ BUG with sides BG = 105, BU = 16 and UG = 30 is 151 units.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
It is given that ΔTOP ~ ΔBUG.
The lengths of sides of ΔTOP is - TO = 16, TP = 20, OP = 30.
The length of one side of ΔBUG is BG = 105.
Since ΔTOP is same as ΔBUG, so sides BU and UG will same as sides TO and OP respectively.
So, BU = 16 and UG = 30.
The formula for the perimeter of a triangle is -
P = a + b + c
Where, P is the perimeter and a, b, c are the sides of the triangle.
For ΔBUG -
P = BU + BG + UG
P = 16 + 105 + 30
P = 151
Therefore, the perimeter of ΔBUG = 151 units.
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Solve the following literal equation for y. -5x+8y=15
need help with questions 6-15 only with all work shown.
Consequently, the square root of the [tex]\sqrt{25}[/tex] is 5 and square root of [tex]\sqrt{4}[/tex] is 2 . The square root and nth root .
what is square root ?The square root or nth root is represented by the radical sign. Square roots are a component of root expressions. There is a radical's radicand—a number or word that appears. Radicals like 7 and 2y+1 serve as examples. Additional terms that describe radicals include: Radical equations are those equations that include radicals. A "root expression" is the phrase used to describe the expression contained within the square root. To demonstrate radical representations, consider the numbers 2, 372, 2x+7, and 41p. The phrase "root expression" refers to the expression contained within the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.
given
square root of (a) [tex]\sqrt{25}[/tex] because 5 is the square root, square root of
as b ) square root of [tex]\sqrt{4}[/tex] s2's square root
Consequently, the square root of the [tex]\sqrt{25}[/tex] is 5 and square root of [tex]\sqrt{4}[/tex] is 2 .
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carlos borrowed 26,000 for 5 years at an APR 5.25% what will his monthly payment be?
Answer:
$568.75.
Step-by-step explanation:
Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42? l'll give brainiest
Answer: x3 +y3 20
Step-by-step explanation:
what is synthetic division method
The figure shows an object O in front of a plane mirror. Determine from which locations A-D the object's image is visible.
O A O B O C O D
An object O is displayed in front of a plane mirror in the figure. The image of the object is visible from locations B and C.
An object's image is created by a plane mirror by reflecting light rays that originate from the object. The object and its image appear to be equally distant from the mirror because the image created by a plane mirror is imaginary, upright, and the same size as the object.
As light from the object enters the plane mirror, it reflects each beam in accordance with the Law of Reflection. At the intersection of the reflected beams' extensions, the image is visible.
Therefore, the location must be on the reflected ray's path for the image to be visible. Here, locations B and C are on the path of the reflected ray. So the image is visible in these locations. But not in locations A and D.
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Cole has many cans of fruit and vegetables in her pantry. 1/4 of the cans are vegetables and 6/7 of the cans are fruit. What fraction of the cans are either fruit or vegetables?
Answer:
Fraction of fruit or vegetable cans = 13/28
Step-by-step explanation:
The fraction of the cans that are either fruit or vegetables is the sum of the fractions of the cans that are fruit and the cans that are vegetables. Since the fractions are for mutually exclusive categories, we can add the fractions of cans of fruit and the cans of vegetables to find the total fraction of cans that are either fruit or vegetables.
Fraction of fruit cans: 6/7
Fraction of vegetable cans: 1/4
Therefore,
Fraction of fruit or vegetable cans = 6/7 + 1/4 = (6 + 7)/(7*4) =13/28
Listed below are the lead concentrations (in mg/g) measured in different samples of a medicine. What do the results suggest about the safety of this medicine? What do the decimal values of the listed amounts suggest about the precision of themeasurements?
O 18.5
O 14.5
O 20.5
O 7.5
O 18
O 8.5
O 8
O 9.5
O 15
The results suggest that the lead concentrations in the medicine samples are relatively low, as all of the values are below 20 mg/g. However, it would be necessary to compare these values to a standard, such as the acceptable limit of lead in medicine set by a regulatory body, in order to determine if the medicine is considered safe.
The decimal values of the listed amounts suggest that the measurements were precise, as they are all reported to one decimal place. It means that the measurement was done with a precision of 0.1. In addition to that, the measurements are consistent and close to each other, which also indicates that the measurements were precise.
It's important to keep in mind that precision and accuracy are different things. Precision refers to the degree of reproducibility of a measurement, while accuracy refers to the degree of closeness of a measurement to the true value. In this case, the measurements are precise but it's not specified if the measurements are accurate or not.
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Please help I don’t understand!
From the curve in the graph the function values are
h(3) = 2
h(5) = 6
h(6) = 5
What is parabolic curve?A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.
The quadratic equation represents a parabolic curve on a graph
Examining the graph the function values can be deduced noting that the values 3 5 6 and in h(3), h(5) and h(6) are points in the x axis or the domain
The function values are points on the y axis corresponding to tracing the x values to the curve
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which of the following could be an example of a function with a domain [a, infinity) and a range (-infinity, b] where a>0 and b>0
f(x) = √x ⇒ f(x) = -√(x -a) +b . . . . . . matches choice B
What is function ?
Function is the relationship between the input or domain and the output. A relation is a function if and only if there exists one value in the range for every domain value. A function is written as f x , where x is the input value. The general form of a function is y = f x
Function transformations
To move the domain from [0, ∞) to [a, ∞) requires the function be translated 'a' units to the right. That transformation is accomplished by replacing x with (x-a) in the function definition.
To move the range from [0, ∞) to [b, ∞) requires the function be translated upward by 'b' units. This is accomplished by adding 'b' to every function value.
Therefore, the range of the function will be (-∞,b] i.e. y ≤ b.
Hence, the required function is f(x) = √x ⇒ f(x) = - √(x -a) +b . . . . . . matches choice B
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Does each equation represent exponential decay or exponential growth?
Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
A = (0.97)t
y=3.7(0.2)t
y= 9/11(4)t
P=7/9(5/4)t
V=0.8(9)t
P=0.9(8.3)t
g(x) = 2.1(x)
Solving the provided question, we can say that Not exponential growth or decay (no exponent) G(x)=1.3(x)
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially.
The base of the exponentiation is the strongest indicator of whether an equation exhibits an exponential growth or decline.
It will be an exponential growth if the base is greater than 1.
It will be an exponential decay if the base is less than 1.
There won't be any exponential growth or decay if the function's exponent is zero.
Therefore: Decay exponential (base less than 1:
W = 9/8(3/5)t
f(t) = (3/4)t
L = 4.2(0.6)t
Exponential Growth (base larger than 1:
L = 0.25(12)t
W = 0.5(2.1)t
f(t) = 2/3(6)t
Not exponential growth or decay (no exponent):
G(x)=1.3(x)
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Suppose that for a graduating class of seniors at a local high school, the average GPA is 3.21. If a sampling distribution of size n = 20 is created from this population of seniors, what would be the expected mean of the sampling distribution?
0.72
1.67
0.161
3.21
Suppose that for a graduating class of seniors at a local high school, the average GPA is 3.21. The expected mean of the sampling distribution would be 3.21.
What is the average GPA?Generally, This is because the sampling distribution of the mean is a probability distribution of the means of all possible samples of the same size from the same population.
The mean of the sampling distribution is equal to the population mean, in this case, 3.21.
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Sara has a 30-gallon fish tank.The tank already has 24 gallons of water in it.Sara adds more water at a rate of 0.5 gallons per minute.
Solving a linear equation we can see that the tank will be filled in 12 minutes.
How long will take Sara to fill the tank?We know that the fish tank has a volume of 30 gallons, and it already has 24 gallons of wate on it.
Sara is adding more water at a rate of 0.5 gallons per minute, so after x minutes, the volume of water on the tank is modeled by the linear equation:
V(x) = 24gal + 0.5gal*x
The tank will be full when the volume is equal to 30 gallons, then we can solve the equation:
30 gal = 24 gal + 0.5gal*x
30 gal - 24gal = 0.5gal*x
6 gal = 0.5gal*x
6gal/0.5gal = x
12 = x
The tank will be full after 12 minutes.
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I need help ASAP
Look at the image below
Answer:
2 only
Step-by-step explanation:
Answer:2 and 4
Step-by-step explanation:
if you divide 164 by all the numbers you only get whole numbers when you divide it by 2 and 4 not 3 and 6
please help me i would be happy if you helped me
The function to represent the arithmetic sequence is y = 0.17x + 0.71, and an envelop weighing 8 ounces cost $2.07
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
An arithmetic sequence is in the form:
[tex]a_n=a_1+(n-1)d\\\\where\ a_1=first\ term,d=common\ difference[/tex]
Let y represent the price to send an envelop of x ounces. The arithmetic sequence is:
y = a₁ + (x - 1)d
Given that the first ounce is 88 cents($0.88), hence a₁ = 0.88. Eadh additional ounce is 17 cents (0.17), hence d = 0.17. Therefore:
y = 0.88 + (x - 1)(0.17)
y = 0.17x + 0.71
For a cost of $2.07:
2.07 = 0.17x + 0.71
x = 8 ounces
The function to represent the arithmetic sequence is y = 0.17x + 0.71
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ILL GIVE BRAINLIEST IF CORRECT NEED HELP ASAP PLS
Answer:
A
Step-by-step explanation:
Answer: y = (3/4)x - (7/4).
Step-by-step explanation:
Subtract 3x from both sides of the equation. Divide both sides of the equation by -4. Simplify. We get that solving 3x - 4y = 7 for y gives y = (3/4)x - (7/4).