Question

In your own words, explain how to find the rate of change of the following graph at x=1. Then find the rate of change at x=1.

Answer 1

Rate of change of the graph = 1

Explanation:

Rate of change of the graph at any point is defined by the slope of the line at that point.

Since, slope of a line between two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

m =
`(y_2-y_1)/(x_2-x_1)=(\triangle y)/(\triangle x)`

In other words, slope of a line between two points is given by the ratio of rise and run of the line between the given points.

Therefore, slope of the line passing through two points (0, 2) and (1, 3) will be,

m =
`(3-2)/(1-0)`

m = 1

Rate of change at x = 1 is 1.