Question

Find the equation of the line through (-5,3) that is parallel to the line through (9,6) (-8,-6)

Answer 1

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.

Step-by-step explanation:

Using the two points (9, 6) and (-8, -6),

Finding the slope,

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ =(-6-6)/(-8-9) \\ =(-12)/(-17) \\ m=(12)/(17) \end{gathered}`

Using the point-slope formula,

`\begin{gathered} y-y_1=m(x-x_1) \\ y-3=(12)/(17)(x-(-5)) \\ 17y-51=12(x+5) \\ 17y-51=12x+60 \\ 12x-17y+51+60=0 \\ 12x-17y+111=0 \end{gathered}`

Therefore, the equation of the line is,

`12x-17y+111=0`

Final answer:

The equation of the line is,

`12x-17y+111=0`