# Math Help - Perpendicular Line/Equation

1. ## Perpendicular Line/Equation

Hi,

I would be grateful if someone could confirm whether the equation of the line perpendicular to the line 10x + 7y = 11 which passes through points (-1, 3) is 7x - 10y = -37?

If not, where have I gone wrong?!

2. Originally Posted by looking0glass
Hi,

I would be grateful if someone could confirm whether the equation of the line perpendicular to the line 10x + 7y = 11 which passes through points (-1, 3) is 7x - 10y = -37?

If not, where have I gone wrong?!

you are right !

3. Hello, looking0glass!

You are right!

You can check your own work . . .

You have: . $7x - 10y \:=\:-37$

Is it perpendicular to $10x + 7y \:=\:15$?

Solve for $y$ . . .

Their line is: . $y \:=\:\text{-}\tfrac{10}{7}x+\tfrac{15}{7}$
. . Its slope is: $m_1 \:=\:\text{-}\tfrac{10}{7}$

Your line is: . $y \:=\:\tfrac{7}{10}x + \tfrac{37}{10}$
. . Its slope is: $m_2\:=\:\tfrac{7}{10}$

Since $m_1\!\cdot\!m_2 \:=\:-1$, the line are perpendicular.

Does your line pass through (-1, 3) ?
Does (-1,3) satisfy your equation?

. . $7(-1) - 10(3) \:=\:-37$ . . . Yes!

Therefore, your equation is correct.