Question

The table represents some points on the graph of a linear function. What is the rate of change of y with respect to x for this function?

X: -15, -10, -5, 0, 5, 10
Y: 5, 2, -1, -4, -7, -10
A. The rate of change is 3.
B. The rate of change is -3.
C. The rate of change is 1/3.
D. The rate of change is -1/3.

Answer 1

The rate of change of y with respect to x for the given linear function is found by calculating the slope using any two points. Upon calculation using the points (0, -4) and (5, -7), the slope, and consequently the rate of change, is -3.

Step-by-step explanation:

The rate of change of y with respect to x in a linear function is the slope of the line. To find the slope, you can use any two points on the line. Using the points (-15, 5) and (-10, 2) from the given table, we calculate the slope as follows:

Slope (m) = (Change in y) / (Change in x) = (y2 - y1) / (x2 - x1) = (2 - 5) / (-10 - (-15)) = (-3) / (5) = -3/5

However, since the options provided are in simplified integer or reciprocal form, we need to use another pair of points that will yield a simplified slope value. Considering the points (0, -4) and (5, -7), we calculate the slope again:

Slope (m) = (Change in y) / (Change in x) = (-7 - (-4)) / (5 - 0) = (-3) / (5) = -3/5, which simplifies to -3

Hence, the correct answer is B. The rate of change is -3.