Find the rate of change of the linear function from the point ​(0​,14​) to the point ​(18​,8​).

Answer 1

so to get the rate of change, we can do two approaches. the first is to simply observe that as x goes from 0 to 18 (change in x = 18) why goes from 14 to 8 (change in y = -6). the rate of change of the function is equal to (rate of change of y/ rate of change of x) which is -6/18 = -3. this means for each positive point change in x, y changes negatively by 3 points.

another way is to write the function y = f(x). since this is linear it has an easy format y = a + bx. we have two values of y and x each so we use them:

14 = a + b * (0)

8 = a + b * (18)

solve together: a = 14 (from first equation). this means 8 = 14 + b * (18) --> b = (8 - 14)/18 = -6/18 = -3. thus b which is the rate of change in a linear function is -3.