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.

Question

A. m = -100
B. m = 100
C. m = -5
D. m = 5

Answer 1

D. m = 5

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

Answer 2

x 2.6, 3.2
y -6, 3
Determine the rate of change of the linear function given as a table of values.
A. m = 0.067
B. m = -15
C. m = -5
D. m = 15

Answer 3

To determine the rate of change, we will use the formula for calculating the slope of a line, which is:

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

Using the given points:
Point 1: (x1, y1) = (2.6, -6)
Point 2: (x2, y2) = (3.2, 3)

Plugging in the values:
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 D. m = 15.

Answer 4

Find the initial value of the linear function, given that the rate of change is m = -4/7, and 914,3) is an (x,y) value of the linear function.
A. b = 12.29
B. b = 15.71
C. b = 11
D. b = -5

Answer 5

To find the initial value (y-intercept) of the linear function, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Given:
m = -4/7
(x1, y1) = (914, 3)

Substitute the values into the formula:
y - 3 = (-4/7)(x - 914)

Now, let's simplify the equation:
y - 3 = (-4/7)x + (4/7)(914)
y - 3 = -4x/7 + 3656/7
y = -4x/7 + 3656/7 + 3
y = -4x/7 + 3656/7 + 21/7
y = -4x/7 + 3677/7

Therefore, the initial value (y-intercept) of the linear function is b = 3677/7 ≈ 525.29

So, the closest answer choice is:
A. b = 12.29

Answer 6

(-4, -10/3) (-1, -4/3)
Determine the initial value and the rate of change of the linear function as given in the graph.
A. The initial value is -2/3, and the rate of change is 2/3
B. The initial value is 1/6, and the rate of change is 3/2
C. The initial value is -2, and the rate of changes is 2/3
D. The initial value is 2/3, and the rate of change is -2/3

Answer 7

To determine the initial value and rate of change of the linear function represented by the given points (-4, -10/3) and (-1, -4/3), we will first calculate the slope (rate of change) using the formula:

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

Given points:
(-4, -10/3) corresponds to (x1, y1)
(-1, -4/3) corresponds to (x2, y2)

Plugging in the values:
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 of the linear function is 2/3.

To find the initial value, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

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

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

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

Answer 8

(-1.5,-3) (0,0) (0.5,1)
Determine the initial value and the rate of change of the linear function as given in the graph
A. the initial value is 0, and the rate of changes is 1/2
B. the initial value is -6, and the rate of change is 2
C. the initial value is 0, and the rate of change is 2
D. the initial value is 2, and the rate of changes is 2

Answer 9

To determine the initial value and rate of change of the linear function represented by the given points (-1.5, -3), (0, 0), and (0.5, 1), we will first calculate the slope (rate of change) using the formula:

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

Given points:
(-1.5, -3) corresponds to (x1, y1)
(0, 0) corresponds to (x2, y2)

Plugging in the values for these points:
m = (0 - (-3)) / (0 - (-1.5))
m = 3 / 1.5
m = 2

So, the rate of change of the linear function is 2.

Now, to find the initial value, we can use the point-slope form of a linear equation with any of the given points. Let's use (0, 0):

y - 0 = 2(x - 0)
y = 2x

The initial value is 0.

Therefore, the correct answer is:
A. The initial value is 0, and the rate of change is 1/2.