Question

Give the equation of a line that goes through the point ( − 24 , 2 ) and is perpendicular to the line 8 x + 3 y = − 6 . Give your answer in slope intercept form

Answer 1

`y=(3)/(8)x+11`

Explanation:

To find a line that is perpendicular to 8x + 3y = -6 and goes through (-24, 2), lets first find what the line's slope would be.

We can find this by finding the slope of 8x + 3y = -6 and taking the negative reciprocal of it.

We can find the slope of that line by putting it in slope-intercept form:

8x + 3y = -6

Subtract 8x from both sides.

3y = -6 - 8x

Divide both sides by 3.

`y=-(6)/(3)-(8)/(3)x`

`y=-(8)/(3)x-2`

So the slope of that line would be -8/3.

The negative reciprocal of -8/3 would be 3/8.

Now we know that the new line would have to pass through the point (-24, 2). We can use this point and write the equation in point-slope form:

`y-2=(3)/(8)(x+24)`

Now lets change this into slope-intercept form. Add 2 to both sides.

`y=(3)/(8)(x+24) +2`

Distribute the 3/8.

`y=(3)/(8)x+9+2`

Simplify.

`y=(3)/(8)x+11`

And now we have our equation in slope-intercept form.

I hope you find this helpful.