Question

The table shows values for points on the graph of a linear function. x −2 1 2 4 y 13 1 −3 −11 What is the slope of the graph of this linear function?

Answer 1

You can find the slope of a linear function by taking two points and finding the change in y over change in x.

Hm, but the values you gave for the tables don't make sense for a linear function/relationship. But let's just pick two points as an example.

So two points you can pick are (-2, 13) and (1, -3).
The slope, change in y over change in x is in other words (y2 - y1 / x2 - x1), where (x1, y1) is one point and (x2, y2) is another.

(-3 - 13) / (1 - -2) = -16/3 = -(16/3)

Or you could have switched up the order of those coordinates but you still get the same answer.
(13 - -3) / (-2 - 1) = 16 / (-3) = -(16/3)