Question

Write the equation of the line that is perpendicular to the line 2x − 3y = 3 and passes through the point (−8, 2).

Answer 1

If two lines are perpendicular, their slopes, m1 and m2 are related by\[m_{1}m_{2}=-1\]Or,\[m_2=\frac{-1}{m_1}\]What is the slope of your given line?

Answer 2

To get you started, take 2x-3y=3 and solve for y.

Answer 3

Okay i solved for y= 2x/3 - 1

Answer 4

@eseidl

Answer 5

so what is the slope of this line?

Answer 6

You have it in the form y=mx+b, where m=slope. What is "m" in your line?

Answer 7

I got m =2/3 and b = -1

Answer 8

@eseidl

Answer 9

Correct. We need a line perpendicular to your line with slope 2/3. A line will be perpendicular to your given line, if and only if it's slope is \[m_{2}=\frac{-1}{\frac{2}{3}}=\frac{-3}{2}\]

Answer 10

So now we have the slope of your perpendicular line. We are also given a point through which this line passes (-8,2). If you know the slope and a point, to find the equation of a line we use "point slope form":\[(y-y_0)=m(x-x_0)\]where m=slope, and (x_0, y_0) is your known point.

Answer 11

Inputting,\[(y-2)=\frac{-3}{2}(x-(-8))\]I'll let you finish.