Question

Use the following table to answer the question
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
m = -0.5, b = 10.5
m = 0.5, b = 5.5
m = -7, b = -3
m = -3, b = -7

Answer 1

To determine the rate of change and initial value of the linear function given the table of values, we need to calculate the slope (m) and the y-intercept (b) for each set of data points.

For the first set of data points (m = -0.5, b = 10.5):
m = (y2 - y1) / (x2 - x1) = (14 - 8) / (-7 - (-5)) = 6 / -2 = -3
b = y1 - m * x1 = 8 - (-5) * -0.5 = 8 + 2.5 = 10.5

For the second set of data points (m = 0.5, b = 5.5):
m = (y2 - y1) / (x2 - x1) = (14 - 8) / (-7 - (-5)) = 6 / -2 = -3
b = y1 - m * x1 = 8 - (-5) * 0.5 = 8 + 2.5 = 10.5

For the third set of data points (m = -7, b = -3):
m = (y2 - y1) / (x2 - x1) = (14 - 8) / (-7 - (-5)) = 6 / -2 = -3
b = y1 - m * x1 = 8 - (-5) * -7 = 8 + 35 = 43

For the fourth set of data points (m = -3, b = -7):
m = (y2 - y1) / (x2 - x1) = (14 - 8) / (-7 - (-5)) = 6 / -2 = -3
b = y1 - m * x1 = 8 - (-5) * -3 = 8 + 15 = 23

The correct answers are:
1. m = -0.5, b = 10.5
2. m = 0.5, b = 5.5