precalculus help

Question

If f(x) is a linear function, f(-3)=2, and f(1)=-4, find an equation for f(x).

f(x) =

Answer 1

Since we know it's a linear function, we need to figure out what info we have. I'm seeing 2 points, (-3, 2) and (1,-4).

Finding a line, we always need to figure out the slope; (change in y) / (change in x)

slope = ((-4)-2)/(1-(-3)) = (-6)/(4) = -1.5

now that we have slope, let's find the y-intercept (b).

y = mx+b

Plugging in (1,-4) and m=-1.5:

-4 = (-1.5)(1) + b

b = -2.5

Combining our results, we get:

f(x) = -1.5x - 2.5