# How do you find a standard form equation for the line with point (-1,12) and is perpendicular to the line is , where 6x - 7y + 3 = 0?

Dec 5, 2017

When given the equation of a line in the standard form,

$A x + B y = C$

you obtain the standard equation form of all lines that are perpendicular by swapping A and B and change the sign of one.

#### Explanation:

Given:

$6 x - 7 y = - 3$

Please observe that $A = 6$ and $B = - 7$

To make the standard form of all lines that are perpendicular, swap A and B and, because B is negative, I shall change the sign of B:

$7 x + 6 y = D$

To find the value of D, evaluate the standard from at the given point, $\left(- 1 , 12\right)$:

$7 \left(- 1\right) + 6 \left(12\right) = D$

$D = 65$

The standard form of the equation of the desired line is:

$7 x + 6 y = 65$

Here is an image with, $6 x - 7 y = - 3$ in red, $7 x + 6 y = 65$ in blue, and $\left(- 1 , 12\right)$ in black: