Final answer:
The slope of the linear function, calculated using the given points (-4, -5) and (4, 0), is 0.625, which does not match any of the provided options, suggesting an error in the question or answer choices.
Step-by-step explanation:
The rate of change of a linear function is determined by calculating the slope of the line that the function represents. The slope is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line.
Using two points from the given data, (-4, -5) and (4, 0), we can calculate the slope (m) as follows:
- Change in Y (rise) = Y2 - Y1 = 0 - (-5) = 5
- Change in X (run) = X2 - X1 = 4 - (-4) = 8
- Slope (m) = rise/run = 5/8 = 0.625
However, none of the options given (a. -0.5, b. 0.5, c. -1, d. 1) match the calculated slope of 0.625. It seems there may be an error with the question or the options provided.