If f(x) is a linear function, f(- 3) = - 3 , and f(5) = 4 , find an equation for f(x)

Question

asked Sep 1, 2021 17.5k views

1 Answer

Kevin MOLCARD · Answer 1 · 2021-09-05T01:24:52+0000

f(x)=mx+b

f(-3)=-3 meaning that (-3,-3)

f(5)=4 meaning that (5,4)

(1 ) Find slope.

$m=(y_2-y_1)/(x_2-x_1)\\m=(4+3)/(5+3)\\m=(7)/(8)$

The slope is 7/8

(2) Substitute any ordered pairs in the equation.

I'll use (5,4)

$f(x) = (7)/(8)x+b\\4=(7)/(8)(5)+b\\4=(35)/(8)+b\\32=35+8b\\32-35=8b\\-3=8b\\-(3)/(8)=b\\b=-(3)/(8)$

Therefore the equation for f(x) is
f(x)=(7)/(8)x-(3)/(8)