Find the equation of the line perpendicular to...

[confused-]

Find the equation of the line perpendicular to 3x - 2y + 6 = 0 and having the same y-intercept.

I can make it -2y = -3x - 6
y = 3/2x + 3
so m = 3/2



but that's where I'm stuck.

 

[pka]

Find the equation of the line perpendicular to 3x - 2y + 6 = 0 and having the same y-intercept.

\(\displaystyle Ax+By+C=0~\&~-Bx+Ay+D=0\) are perpendicular lines.
In your case you need (0,3) on both lines.

 

[fasteddie65]

If m = 3/2 for the given line, a line perpendicular to it would have slope -2/3. With a y-intercept 3, an equation is y = (-2/3)x + 3, or 3y = -2x + 9, or 2x + 3y = 9.

 

[mmm4444bot]

\(\displaystyle Ax+By+C=0~\&~-Bx+Ay+D=0\) are perpendicular lines.

Clever! (Two mental steps, and you're at the answer quickly.)