Answer:
[tex]f(x)=\frac{3}{2}x-2[/tex]
Step-by-step explanation:
step 1
Find the slope m
we have
(-2,-5) and (4,4)
The slope is equal to
[tex]m=\frac{4+5}{4+2}[/tex]
[tex]m=\frac{9}{6}[/tex]
simplify
[tex]m=\frac{3}{2}[/tex]
step 2
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{2}[/tex]
[tex](4,4)[/tex]
substitute
[tex]y-4=\frac{3}{2}(x-4)[/tex]
step 3
Convert to slope intercept form
[tex]y-4=\frac{3}{2}(x-4)[/tex]
[tex]y=\frac{3}{2}x-6+4[/tex]
[tex]y=\frac{3}{2}x-2[/tex]
Convert to function notation
[tex]f(x)=\frac{3}{2}x-2[/tex]
