Answer:
[tex]y=\frac{1}{3}x+3[/tex]
Step-by-step explanation:
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
we have the points
(−6, 1) and (3, 4)
substitute the value of x and the value of y of each point in the equation of the line, then solve for m and b
For (-6,1)
[tex]1=-6m+b[/tex] ----->[tex]b=6m+1[/tex] -----> equation A
For (3,4)
[tex]4=3m+b[/tex] ----> [tex]b=-3m+4[/tex] -----> equation B
Solve the system of equations A and B
Match equation A and equation B
[tex]6m+1=-3m+4[/tex]
Solve for m
[tex]6m+3m=4-1[/tex]
[tex]9m=3[/tex]
[tex]m=\frac{1}{3}[/tex]
Find the value of b
[tex]b=6(\frac{1}{3})+1[/tex]
[tex]b=3[/tex]
The equation of the line is
[tex]y=\frac{1}{3}x+3[/tex]
