Find slope of AB where A = (-1,-3) and B = (5,2):
[tex]\text {Slope = } \dfrac{Y_2-Y_1}{X_2-X_1} [/tex]
[tex]\text {Slope = } \dfrac{2+3}{5+1} = \dfrac{5}{6} [/tex]
Write equation with the slope found:
[tex]y = mx + b[/tex]
[tex]y = \dfrac{5}{6} x + b[/tex]
Find y-intercept:
[tex]y = \dfrac{5}{6} x + b[/tex]
[tex]2 = \dfrac{5}{6} (5) + b[/tex]
[tex]2 = \dfrac{25}{6} + b[/tex]
[tex]b = 2 - \dfrac{25}{6}[/tex]
[tex]b = -\dfrac{13}{6}[/tex]
Form the equation:
[tex]y = \dfrac{5}{6} x - \dfrac{13}{6}[/tex]
[tex]\boxed {\boxed {\bf \text {Answer: Line AB : }y = \dfrac{5}{6} x - \dfrac{13}{6}}}[/tex]
Find Slope of Line MN where MN is parallel to AB:
[tex]\text {Slope of MN = Slope of AB = } \dfrac{5}{6}[/tex]
Write equation with the slope found:
[tex]y = mx + b[/tex]
[tex]y = \dfrac{5}{6} x + b[/tex]
Find y-intercept given that the line passed through (6, -2):
[tex]y = \dfrac{5}{6} x + b[/tex]
[tex]-2 = \dfrac{5}{6} (6) + b[/tex]
[tex]-2 =5 + b[/tex]
[tex]b = -2 - 5[/tex]
[tex]b = -7[/tex]
[tex]
\boxed {\boxed {\bf \text {Answer: Line MN } : y = \dfrac{5}{6} x -7 }}[/tex]
