[tex]f(x)=mx+b[/tex]
[tex]f(-3)=-3[/tex] meaning that (-3,-3)
[tex]f(5)=4[/tex] meaning that (5,4)
(1 ) Find slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{4+3}{5+3}\\m=\frac{7}{8}[/tex]
The slope is 7/8
(2) Substitute any ordered pairs in the equation.
I'll use (5,4)
[tex]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}[/tex]
Therefore the equation for f(x) is [tex]f(x)=\frac{7}{8}x-\frac{3}{8}[/tex]
