Answer:
The equation in point slope form is [tex]y-6=\frac{1}{3}(x-4)[/tex]
The equation in slope intercept form is [tex]y=\frac{1}{3}x-\frac{14}{3}[/tex]
Step-by-step explanation:
step 1
Find the slope m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex](-5,3),(4,6)[/tex]
Substitute the values
[tex]m=\frac{6-3}{4+5}[/tex]
[tex]m=\frac{3}{9}[/tex]
simplify
[tex]m=\frac{1}{3}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{3}[/tex]
[tex](4,6)[/tex]
substitute
[tex]y-6=\frac{1}{3}(x-4)[/tex] ---> equation in point slope form
step 3
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
[tex]y-6=\frac{1}{3}(x-4)[/tex] ----> convert to slope intercept form
[tex]y-6=\frac{1}{3}x-\frac{4}{3}[/tex]
[tex]y=\frac{1}{3}x-\frac{4}{3}+6[/tex]
[tex]y=\frac{1}{3}x-\frac{14}{3}[/tex]
