Answer: f(x) = 2x - 3
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We're given f(-1) = -5 and f(5) = 7
This means we know the two points (-1,-5) and (5,7) are on the line.
Find the slope
m = (y2-y1)/(x2-x1)
m = (7-(-5))/(5-(-1))
m = (7+5)/(5+1)
m = 12/6
m = 2
The slope is 2.
Use this along with (x1,y1) to find the equation. We'll use point slope form
y - y1 = m(x - x1)
y - (-5) = 2(x - (-1))
y + 5 = 2(x + 1)
y = 2x + 2 - 5
y = 2x - 3
f(x) = 2x - 3
