Question

Use the table to answer the question.

x y
1 4
−3 8

Find the rate of change and the initial value of the linear function given as a table of values. (1 point)

The rate of change is m=_____ and the initial value is b= _____.

Answer 1

To find the rate of change (m) and the initial value (b) of the linear function, we need to use the formula for slope (m) in the slope-intercept form of a linear equation (y = mx + b).

The rate of change (m) can be found by taking the difference in y-coordinates and dividing it by the difference in x-coordinates:
m = (change in y) / (change in x)

Using the two points given in the table: (1, 4) and (-3, 8)
Change in y = 8 - 4 = 4
Change in x = -3 - 1 = -4

m = 4 / -4 = -1

So, the rate of change is -1.

To find the initial value (b), we can substitute one of the points into the slope-intercept form (y = mx + b) and solve for b:
4 = (-1)(1) + b
4 = -1 + b
b = 4 + 1
b = 5

Therefore, the initial value is 5.

The rate of change is m = -1 and the initial value is b = 5.