The form of the equation of the line is
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept
In order to find the equation of the line first, we need to find the slope using the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where m is the slope, (x1,y1) and (x2,y2) are points where the line passes through
in our case
(-3,4)=(x1,y1)
(3,1)=(x2,y2)
we substitute the values
[tex]m=\frac{1-4}{3+3}=\frac{-3}{6}=-\frac{1}{2}[/tex]Then we need to find the y-intercept so we will use the form of the line we will use x=3 and y=1
[tex]1=-\frac{1}{2}(3)+b[/tex]then we isolate the b
[tex]b=1+\frac{3}{2}=\frac{5}{2}[/tex]ANSWER
The equation of the line is
[tex]y=-\frac{1}{2}x+\frac{5}{2}[/tex]
