Let f be a linear function where f(2) = -5 and f(-3) = 1. Find f(x).

I really do not understand what the question is for this and I am not trying to cheat, I just need to know how to solve this, thank you.

The given information tells you that the graph of the function contains the points (2, -5) and (-3, 1). You can use the same procedure as the one for finding the equation of a line passing through two points.

First find the slope.

m = (y2 - y1) / (x2 - x1)
m = (1 - (-5)) / (-3 - 2)
= 6 / -5
m = -6/5

You can either use slope intercept form or point slope form. I'll use point slope form.

y - y1 = m(x - x1) [I'm using (-3, 1). You can use the other point if you want]
y - 1 = -6/5 (x - (-3)) iff
y - 1 = -6/5 (x + 3) iff
y - 1 = -6/5 x - 18/5 iff
y = -6/5 x - 13/5

Thus the function f(x) = -6/5 x - 13/5

Edit: Using slope intercept form.
Again using (-3, 1) as the point,

y = mx + b
1 = (-6/5)(-3) + b iff
1 = 18/5 + b iff
b = -13/5

Thus y = -6/5 x - 13/5 and f(x) = -6/5 x - 13/5.

your ordered pairs are
(2, -5) and (-3, 1)
change in y, -5 → 1, up 6
change in x, 2 → -3, down 5 ∙ ∙ ∙ ∙ ∙ so slope is -6/5

y – 1 = (-6/5)(x + 3)
y = (-6/5)x – 18/5 + 1
y = (-6/5)x – 18/5 + 5/5
f(x) = (-6/5)x – 13/5

this is just equation of the line through the 2 points

(2, - 5) and (- 3,1)

m = (1 --5)/(- 3 - 2) = 6/- 5 = - 6/5

y = mx + b

- 5 = (- 6/5)(2) + b
- 5 = - 12/5 + b
- 25/5 + 12/5 = b
- 13/25 = b

y = - 6/5x - 13/25