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Write the answer in a slope intercept form Y=Mx + b with all fractions written in lowest terms

Write the answer in a slope intercept form Y=Mx + b with all fractions written in-example-1

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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:


-(1)/((1)/(3))=-3.

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}

Answer:


y=-3x-10.

User Atul Balaji
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