# What is the slope of the linear function if f(2)=-6 and f(-2)=4 ?

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Let the linear function be f(c) = ax + b.

y = ax + b is in the slope intercept form with the slope being a.

We have f(2) = -6 and f(-2) = 4

2a + b = -6 ...(1)

-2a + b = 4 ...(a)

(1) - (2)

=> 4a = -10

=> a = -10/4

=> a = -5/2

**The slope of the linear function is -5/2.**

From enunciation, we conclude that we have two points (2,-6) and (-2,4) that are located on the graph of the linear function f(x).

We'll put 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) = -6, we'll substitute x by 2 in the expression of the linear function:

f(2) = 2m + n

2m + n = -6

n = -6 - 2m (1)

If f(-2) = 4, we'll substitute x by -2 in the expression of the linear function:

f(-2) = -2m + n

-2m + n = 4

n = 4 + 2m (2)

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

-6 - 2m = 4 + 2m

We'll move 2m to the left:

-2m - 2m - 6 = 4

We'll add -6 both sides:

-4m = 10

**m = 10/-4**

**m = -5/2**

**The slope of the linear function is m = -5/2.**