Answer:
Step-by-step explanation:
[tex]y=mx+b[/tex]
[tex]m[/tex] is the slope, [tex]b[/tex] is the y-intercept
in order for the lines to be parallel they must have the same [tex]m[/tex]. we can find the slope of MN by subtracting [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex],
[tex]x_{2}=3[/tex], [tex]x_{1}=-6[/tex], [tex]y_{2} =-5[/tex], [tex]y_{1}= 1[/tex]
[tex]\frac{-5-1}{3+6} =\frac{-6}{9} =-\frac{1}{3}[/tex] is your slope.
Now write the equation as [tex]y=-\frac{1}{3} x+b[/tex] and for your [tex]x[/tex] and [tex]y[/tex] values use Point P: (6,1)
[tex]1=-\frac{1}{3}(6) +b[/tex]
[tex]1=-2+b[/tex]
[tex]3=b[/tex]
Final equation: [tex]y=-\frac{1}{3} +3[/tex]
