If f ( x ) is a linear function

Question

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

f(x)=

Answer 1

y = -4 when x = -1

y = 4 when x = 4

the two points are (-1,-4) and (4,4)

a line through them has slope = (4--4)/(4--1) = 8/5

the equation is

y-4 = (8/5)(x-4) in point slope form

f(x) = (8/5)(x-4) +4

f(x) = 8x/5 -32/5 +20/5

f(x) = 8x/5 -12/5

y =(8/5)x-12/5 in slope intercept form,

8/5=slope, - 12/5 = intercept

5y = 8x -12

8x-5y = 12 in standard form