Question

What is the rate of change of y with respect to x for this function? -4,7 and 4,1


c.3/4
b.-7/9
a.7/9
d.-3/4

Answer 1

To find the rate of change of \( y \) with respect to \( x \), we can use the formula for the slope between two points on a Cartesian plane. The slope \( m \) between the points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

Given the points \( (-4, 7) \) and \( (4, 1) \):

- Let \( (x_1, y_1) = (-4, 7) \)
- Let \( (x_2, y_2) = (4, 1) \)

Substituting in the values:

\[
m = \frac{1 - 7}{4 - (-4)}
\]
\[
m = \frac{-6}{4 + 4}
\]
\[
m = \frac{-6}{8}
\]
\[
m = -\frac{3}{4}
\]

Thus, the rate of change of \( y \) with respect to \( x \) is \( -\frac{3}{4} \).

The correct answer is \( \boxed{d. -\frac{3}{4}} \).