Find the slope of the linear function if f(2)=-9 and f(3)=9?

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

From enunciation, we conclude that we have two points (2,-9) and (3,9) that are located on the graph of the linear function f(x).

We'll write the linear function in the point slope form:

f(x) = mx + n, where m is the slope and n is the y intercept.

If f(2) = -9, we'll substitute x by 2 in the expression of the linear function:

f(2) = 2m + n

2m + n = -9

n = -9 - 2m (1)

If f(3) = 9, we'll substitute x by 3 in the expression of the linear function:

f(3) = 3m + n

3m + n = 9

n = 9 - 3m (2)

We'll put (1) = (2):

-9 - 2m = 9 - 3m

3m - 2m - 9 = 9

m = 9 + 9

m = 18

The slope of the linear function is m = 18.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

A linear function can be written in the form f(x) =ax+b.

Given the values f(2) = -9 and f(3) = 9.

f(-3) = 9 gives a(-3)+b = -9.

-3a+b = -9.....(1).

f(3) = 9 gives: a(3)+b = 9. Or

3a+b = 9.......(2)