Question

Determine the rate of change of the linear function given the table below.

| x | y |
|-3|-10|
|-2| -7 |
|-1| -4 |
|0 | -1 |
| 1 | 2 |

m=[ ]

show work

Answer 1

To find the rate of change (slope) of the linear function, we need to calculate the change in y divided by the change in x:

Change in y = y2 - y1
Change in x = x2 - x1

For the points (-3, -10) and (-2, -7):
Change in y = -7 - (-10) = 3
Change in x = -2 - (-3) = 1

Therefore, the slope for these two points is:
m1 = Change in y / Change in x
m1 = 3 / 1
m1 = 3

For the points (-2, -7) and (-1, -4):
Change in y = -4 - (-7) = 3
Change in x = -1 - (-2) = 1

Therefore, the slope for these two points is:
m2 = Change in y / Change in x
m2 = 3 / 1
m2 = 3

For the points (-1, -4) and (0, -1):
Change in y = -1 - (-4) = 3
Change in x = 0 - (-1) = 1

Therefore, the slope for these two points is:
m3 = Change in y / Change in x
m3 = 3 / 1
m3 = 3

For the points (0, -1) and (1, 2):
Change in y = 2 - (-1) = 3
Change in x = 1 - 0 = 1

Therefore, the slope for these two points is:
m4 = Change in y / Change in x
m4 = 3 / 1
m4 = 3

Since the slope is the same for all pairs of points, the rate of change of the linear function is m = 3.