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Olliej · Answer 1 · 2023-07-13T07:31:40+0000

Recall that two lines are perpendicular if the product of their slopes is equal to -1.

Taking the given equation to its slope-intercept form we get:

$\begin{gathered} (3y)/(3)=(x)/(3)+(4)/(3), \\ y=(x)/(3)+(4)/(3)\text{.} \end{gathered}$

Therefore the slope of the given line is 1/3, therefore, the slope of a perpendicular line to the given line is:

Now we will use the following slope-point formula for the equation of a line:

$y-y_1=s(x-x_1)\text{.}$

Substituting s=-3 and (x₁,y₁)=(-6,8) we get:

$y-8=-3(x-(-6))\text{.}$

Simplifying the above equation we get:

$\begin{gathered} y-8=-3(x+6), \\ y-8=-3x-18. \end{gathered}$

Adding 8 to the above equation we get:

$\begin{gathered} y-8+8=-3x-18+8, \\ y=-3x-10. \end{gathered}$

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