Question

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

Answer 1

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.`