Given:
The line passes through the point (-5, 3) and is parallel to the line through (9, 6) and (-8, -6).
To find:
The line of the equation.
Explanation:
Using the two points (9, 6) and (-8, -6),
Finding the slope,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-6-6}{-8-9} \\ =\frac{-12}{-17} \\ m=\frac{12}{17} \end{gathered}[/tex]
Using the point-slope formula,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{12}{17}(x-(-5)) \\ 17y-51=12(x+5) \\ 17y-51=12x+60 \\ 12x-17y+51+60=0 \\ 12x-17y+111=0 \end{gathered}[/tex]
Therefore, the equation of the line is,
[tex]12x-17y+111=0[/tex]
Final answer:
The equation of the line is,
[tex]12x-17y+111=0[/tex]
