Find the line perpendicular to -2x-3y=9 and goes through the points (-6,-4)

Question

Give the equation of a line that goes through the point (-6,-4) and is perpendicular to the

line -2x-3y=9. Give your answer in slope intercept form.

Answer 1

I would start this problem by rewriting this equation into something that's a little easier to graph and understand. Let's use the slope-intercept formula, y = mx + b

So we start with

-2x-3y=9

-3y=9+2x

y=(9/-3)+(2/-3)x

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

y=(-2/3)x-3, so our slope m=(-2/3)

A perpendicular line has a slope that is the negative reciprocal of the line it makes a right angle with. So that means flip the sign and flip the number.

When we flip the sign of our slope, we get a positive (2/3).

Then we flip the number and get (3/2).

So the slope for our perpendicular line is (3/2).

Now, we plug our new slope and our given point of (-6, -4) back into the slope-intercept formula

y=mx+b --> -4 = (3/2)(-6) + b

-4 = -9 + b

5 = b

Now, that we've used our given point to find b (b represents the place where the line crosses the y-axis, also called the y-intercept), we can use everything we've found out to write the equation of the perpendicular line at any point (x,y)

y = mx + b

y = (3/2)x + 5

If we want to rearrange it to look more like the original equation, it would be

y = (3/2)x + 5

-(3/2)x + y = 5