Question

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

Answer 1

`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)`