Determine the rate of change in the following description. In Ms. Katy’s math class, a homework assignment is worth 100 points. If students turn the homework in late, there will be a deduction of 5 points per day. (1 point)

Question

Responses

m=100
m equals 100

m=−100
m equals negative 100

m=−5
m equals negative 5

m=5?

Answer 1

m = -5 points/day

The rate of change is a deduction of 5 points per day for late homework.

Answer 2

Slope and y-intercepts Quick Check
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Question
Use the table to answer the question.

x y
2.6 −6
3.2 3
Determine the rate of change of the linear function given as a table of values.

(1 point)
Responses

m=0.067
m equals 0.067

m=15
m equals 15

m=−15
m equals negative 15

m=−5

Answer 3

To determine the rate of change (slope) between the two points in the table, we use the formula:

m = (y2 - y1) / (x2 - x1)

Let's calculate:

m = (3 - (-6)) / (3.2 - 2.6)
m = (3 + 6) / 0.6
m = 9 / 0.6
m = 15

Therefore, the rate of change of the linear function given by the table of values is:

m = 15

So, the correct response is: m = 15

Answer 4

Find the initial value of the linear function, given that the rate of change is m=−47, and (14,3) is an (x,y) value of the linear function.(1 point)
Responses

b=15.71
b equals 15.71

b=11
b equals 11

b=12.29
b equals 12.29

b=−5

Answer 5

To find the initial value (y-intercept) of the linear function, we can use the slope-intercept form formula y = mx + b, where m is the slope and b is the y-intercept.

Given that the rate of change (slope) is m = -47, and the point (14,3) lies on the line, we can plug these values into the formula:

3 = -47(14) + b
3 = -658 + b
b = 3 + 658
b = 661

Therefore, the initial value of the linear function is b = 661.

So, the correct response is: b = 661

Answer 6

pick one

Answer 7

b = 661

Answer 8

Find the initial value of the linear function, given that the rate of change is m=−4/7 , and (14,3) is an (x,y) value of the linear function.(1 point)
Responses

b=15.71
b equals 15.71

b=11
b equals 11

b=12.29
b equals 12.29

b=−5

Answer 9

To find the initial value (y-intercept) of the linear function, we can use the slope-intercept form formula y = mx + b, where m is the slope and b is the y-intercept.

Given that the rate of change (slope) is m = -4/7, and the point (14,3) lies on the line, we can plug these values into the formula:

3 = (-4/7)(14) + b
3 = (-56/7) + b
3 = -8 + b
b = 3 + 8
b = 11

Therefore, the initial value of the linear function is b = 11.

So, the correct response is: b = 11

Answer 10

Slope and y-intercepts Quick Check
4 of 54 of 5 Items

Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: left parenthesis negative 4 comma start fraction negative 10 over 3 end fraction right parenthesis, and left parenthesis negative 1 comma start fraction negative 4 over 3 end fraction right parenthesis.

Determine the initial value and the rate of change of the linear function as given in the graph.

(1 point)
Responses

The initial value is −2/3, and the rate of change is 2/3.
The initial value is negative Start Fraction 2 over 3 End Fraction , and the rate of change is Start Fraction 2 over 3 End Fraction .

The initial value is −2, and the rate of change is 2/3.
The initial value is negative 2 , and the rate of change is Start Fraction 2 over 3 End Fraction .

The initial value is 1/6, and the rate of change is 3/2.
The initial value is Start Fraction 1 over 6 End Fraction , and the rate of change is Start Fraction 3 over 2 End Fraction .

The initial value is 2/3, and the rate of change is −2/3.

Answer 11

To determine the initial value and rate of change of the linear function represented by the given graph, we need to use the two points provided: (-4, -10/3) and (-1, -4/3).

First, calculate the slope (rate of change):
m = (change in y) / (change in x)
m = (-4/3 - (-10/3)) / (-1 - (-4))
m = (-4/3 + 10/3) / (3)
m = 6/3 / 3
m = 2 / 3

So, the rate of change is 2/3.

Next, we substitute one of the points into the slope-intercept form equation y = mx + b to find the initial value (y-intercept).

Using the point (-4, -10/3):
-10/3 = (2/3)(-4) + b
-10/3 = -8/3 + b
b = -10/3 + 8/3
b = -2/3

Therefore, the initial value is -2/3, and the rate of change is 2/3.

The correct response is:
The initial value is -2/3, and the rate of change is 2/3.