Question

The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers. The points on the graph are (-7,6) and (7, -4)

What is the rate of change of y with respect to x for this line?

A: 3/7

B: 2/3

C: -7/5

D: -5/7

Answer 1

To find the rate of change of \( y \) with respect to \( x \) (also known as the slope of the line), we use the formula for the slope \( m \):

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

Given the points (-7, 6) and (7, -4), we can assign:

- \( (x_1, y_1) = (-7, 6) \)
- \( (x_2, y_2) = (7, -4) \)

Now, we can substitute these values into the slope formula:

\[
m = \frac{-4 - 6}{7 - (-7)}
\]

Calculating the numerator:

\[
-4 - 6 = -10
\]

Calculating the denominator:

\[
7 + 7 = 14
\]

Putting it all together:

\[
m = \frac{-10}{14} = \frac{-5}{7}
\]

Thus, the rate of change of \( y \) with respect to \( x \) for this line is:

\[
\boxed{-\frac{5}{7}}
\]

The correct answer is D: -5/7.