Question

Use the table to answer the question. Figuring out the starting value and rate of change from a given value table. 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=−0.5, b=5.5 m equals negative 0.5 comma b equals 5.5 m=−7, b=−3 m equals negative 7 comma b equals negative 3 m=−3, b=−7 m equals negative 3 comma b equals negative 7 m=−0.5, b=10.5

Answer 1

To determine the rate of change (slope \( m \)) and the initial value (y-intercept \( b \)) of the linear function defined by the given points, we can follow these steps:

We have the points (-5, 8) and (-7, 14).

1. **Find the rate of change (slope \( m \))** using the formula:

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

Here, \((x_1, y_1) = (-5, 8)\) and \((x_2, y_2) = (-7, 14)\):

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

2. **Find the initial value (y-intercept \( b \))** using the formula \( y = mx + b \). We can plug in one of the points to find \( b \). Using the point (-5, 8):

\[
8 = -3(-5) + b
\]
\[
8 = 15 + b
\]
\[
b = 8 - 15 = -7
\]

So, the rate of change \( m = -3 \) and the initial value \( b = -7 \).

Thus, the answer is:
**m = -3, b = -7**.

This matches the response:
**m = -3, b = -7**.