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.

$m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{4+3}{5+3}\\m=\frac{7}{8}$

The slope is 7/8

(2) Substitute any ordered pairs in the equation.

I'll use (5,4)

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

Therefore the equation for f(x) is $f(x)=\frac{7}{8}x-\frac{3}{8}$