# linear functionCalculate the slope of the linear function if f(2)=-9 and f(3)=9

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You may use the slope equation, such that:

`m = (y_2 - y_1)/(x_2 - x_1)` (`m` represents the slope of the line)

The problem provides `(x_1,y_1) = (2,-9)` and `(x_2,y_2) = (3,9)` , hence, you may substitute the given values of coordinates in slope equation, such that:

`m = (9 - (-9))/(3 - 2) => m = 18/1 => m = 18`

Hence, evaluating the slope of the line that passes through the points `(2,-9)` and `(3,9)` yields `m = 18.`

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.