Question

What is the equation of the line that passes through `(-3,1)` and is perpendicular to the line that passes through the following points: `(-2,4),(6,1)`?

Answer 1

`y=8/3x+9`

Explanation:

Begin by first finding the slope between `(-2,4)` and `(6,1)` by using the slope formula: `m=(y_2-y_1)/(x_2-x_1)`

If we let `(-2,4)-> (color(red)(x_1),color(blue)(y_1))` and `(6,1)-> (color(red)(x_2),color(blue)(y_2))` then,

`m=color(blue)((1-4))/color(red)((6-(-2)))= -3/8`

Since we are looking for the perpendicular slope we use the following: `m_|_=-1/m`

`m_|_=-1/(-3/8)=8/3`

Now that we have our slope `(8/3)` and given the point `(-3,1)` we can find the equation of the line by using the point-slope formula: `y-y_1=m(x-x_1)`

`y-1=8/3(x-(-3)) ->y-1=8/3(x+3)`

We can rewrite this into `y=mx+b` form if desirable

`y=8/3x+8/3*3/1+1 -> y=8/3x+24/3+3/3 -> y=8/3x+27/3`

Upon further simplification, our final answer is `y=8/3x+9`