Use the table to answer the question.

Question

x
y
−5
8
−7
14
Determine the rate of change and the initial value of the linear function given here as a table of values.

(1 point)
Responses

m=−7, b=−3
m equals negative 7 comma b equals negative 3

m=−0.5, b=5.5
m equals negative 0.5 comma b equals 5.5

m=−0.5, b=10.5
m equals negative 0.5 comma b equals 10.5

m=−3, b=−7
m equals negative 3 comma b equals negative 7

Answer 1

To determine the rate of change (m) and the initial value (b) of the linear function given the table of values:

We have the points:

1. (-5, 8)
2. (-7, 14)

The rate of change (slope) \( m \) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (-5, 8) and (-7, 14):

• \( (x_1, y_1) = (-5, 8) \)
• \( (x_2, y_2) = (-7, 14) \)

Substituting the values into the formula:

\[ m = \frac{14 - 8}{-7 - (-5)} = \frac{6}{-2} = -3 \]

Now we can find the initial value \( b \) using the slope-intercept form of a line \( y = mx + b \). We can substitute one of the points into this equation to solve for \( b \). Let's use the point (-5, 8):

\[ 8 = -3(-5) + b \]

Calculating this:

\[ 8 = 15 + b \] \[ b = 8 - 15 = -7 \]

Thus, the rate of change (m) is -3 and the initial value (b) is -7. Therefore, the answer is:

m=−3, b=−7