Question

Find the equation of the line through the point (-2,3) and perpendicular to the line 2x+3y=12. Write the final answer in slope intercept form.

Answer 1

so 2x+3y = 12,

3y = -2x + 12,

y = -2/3 x + 4.

So now what is the slope of this line?

Answer 2

remember:
y = mx +b
where:
m is the slope.
b is the y-intercept

Answer 3

The slope is now -2/3, right?

Answer 4

Yes. the slope is -2/3.

Hmm.. so you have any idea of what is the product of slopes of perpendicular lines?

Answer 5

I honestly don't know where to go from here...

Answer 6

Ok there is a concept here.

Answer 7

"The products of slopes of perpendicular lines equals -1."

Answer 8

Is -2/3x+5/3 correct?

Answer 9

Or you can use \[m_1m_2=-1\]
Is this familiar to you?

Answer 10

\[m_1=current~slope \\ \\ m_2=perpendicular~slope\]

Answer 11

isn't the slope, since it is a perpendicular line, = -3/2 ?

Answer 12

So,
\[(-\frac{2}{3})(m_2)=-1 \\ \\ m_2=\frac{3}{2}\]

Answer 13

Form a new equation using the point-slope form with \(m_2\) and coordinate (-2,3)
\[y-y_1=m_2(x-x_1)\]

Answer 14

\[y-3=\frac{3}{2}(x-(-2)) \\ \\ y=\frac{3}{2}x+3+3 \\ \\ y=\frac{3}{2}x+6\]

Answer 15

Do you get it? @ebeverly

Answer 16

I'll have to rework the problem. I got a completely different answer, but this is super helpful. Thank you very much!

Answer 17

Alright, yw :)