If f (x) is a linear function, f (-2) = 4. and f (3) = -3, find an equation for f (x).

f (x) = - 7/5 x + 6/5

Step-by-step explanation:

We know that, y = mx + c; where c is the y-intercept.

Given, f (-2) = 4 and f (3) = - 3

So, the slope will be, (-3-4) / (3 - (-2)) = - 7/5

Now, find the value of c:

c = y - mx

= 4 - (-7/5) X - 2

= 6/5

So the linear equation will be,

y = - 7/5 x + 6/5

f (x) = - 7/5 x + 6/5