Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b form.

Question

Points are -3,-1 and 2,4

Answer 1

First, calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)
m = (4 - (-1)) / (2 - (-3))
m = 5 / 5
m = 1

Now, substitute one of the points into the equation y = mx + b to solve for b. Let's use the point (-3, -1):

-1 = 1(-3) + b
-1 = -3 + b
b = 2

Therefore, the equation of the linear function is:
y = x + 2

Answer 2

Yesterday, Esperanza worked for 6 hours and earned $120. Today, Esperanza worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns. Enter your answer in y=mx+b form.

Answer 3

Let's assume the number of hours Esperanza worked is represented by x and the amount of money she earned is represented by y.

We have the points (6, 120) and (8, 156). Let's first calculate the slope (m) using these points:

m = (y2 - y1) / (x2 - x1)
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18

Now, let's substitute one of the points to solve for b. Let's use the point (6, 120):

120 = 18(6) + b
120 = 108 + b
b = 12

Therefore, the equation of the linear function is:
y = 18x + 12

Answer 4

Interpret the equation y=−4x+10. What type of function does this equation define? Describe its graph.(1 point)
Responses

This is a nonlinear function. Its graph has a maximum at (0,10).
This is a nonlinear function. Its graph has a maximum at left parenthesis 0 comma 10 right parenthesis .

This is a nonlinear function. Its graph is a curve.
This is a nonlinear function. Its graph is a curve.

This is a linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
This is a linear function. Its graph is a straight line with a slope of negative 4 and a y -intercept of 10.

This is a linear function. Its graph is a straight line with a y-intercept of −4 and a slope of 10.

Answer 5

This is a linear function. Its graph is a straight line with a slope of -4 and a y-intercept of 10.

Answer 6

The equation of a function is y=2x−6 . If this function were graphed, what would its y -intercept be?(1 point)
Responses

2
2

−6
negative 6

6
6

−3
negative 3

Answer 7

The y-intercept of the function y = 2x - 6 is -6. So, the correct answer is:

-6

Answer 8

Equations of Linear Functions Quick Check
3 of 53 of 5 Items
Question
Use the table to answer the question.

x y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.

(1 point)
Responses

y=x+34
y equals x plus 34

y=10x−2
y equals 10 x minus 2

y=−10x+78
y equals negative 10 x plus 78

y=10x+2

Answer 9

First, calculate the slope of the linear function using the points (4, 38) and (6, 58):

m = (y2 - y1) / (x2 - x1)
m = (58 - 38) / (6 - 4)
m = 20 / 2
m = 10

Now, substitute one of the points into the equation y = mx + b to solve for the y-intercept (b). Let's use the point (4, 38):

38 = 10(4) + b
38 = 40 + b
b = -2

Therefore, the equation of the linear function is:
y = 10x - 2

So, the correct answer is:
y = 10x - 2

Answer 10

iwia is opening a bank account. She learns that there is a special promotion where if she deposits $3,000 and then makes no additional deposits or withdrawals, her account will earn $3 in interest per month. Write the equation of a linear function that models the relationship between number of months and total amount of money Oliwia will have in her account.(1 point)
Responses

y=3x+1,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3 x plus 1,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

y=3x+3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3 x plus 3,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

y=3,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

y=1,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 1,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.

Answer 11

To calculate the total amount of money in Oliwia's account, we need to consider the initial deposit of $3,000 and the $3 in interest earned each month. The total amount of money (y) she will have in her account after x months can be represented by the equation:

y = 3x + 3000,

So, the correct answer is:

y = 3x + 3000, where x is the number of months and y is the total amount of money Oliwia will have in her account.

Answer 12

Write the equation of the linear function shown on the graph.

(1 point)
Responses

y=2x−2
y equals 2 x minus 2

y=−2x+2
y equals negative 2 x plus 2

y=−2x−2
y equals negative 2 x minus 2

y=2x+2

Answer 13

Without seeing the graph, I cannot provide the exact equation of the linear function. However, based on the answer choices provided, the correct equation for the linear function shown on the graph depends on the slope and y-intercept it represents.

If the line has a slope of 2 and a y-intercept of -2, then the correct equation would be: y = 2x - 2

Therefore, the correct response would be: y = 2x - 2