How do you find a standard form equation for the line with (−1, −3); perpendicular to the line 2x + 7y + 5 = 0?

Mar 11, 2017

$\left(y + 3\right) = \frac{7}{2} \left(x + 1\right)$

Explanation:

The slope of the given equation graphs out to be $- \frac{2}{7}$ after switching some things around in the equation

$2 x + 7 y + 5 = 0$

$y = - \frac{2}{7} x - \frac{5}{7}$

The slope of the perpendicular line is the negative reciprocal of this slope

$m = - \frac{1}{- \frac{2}{7}} = \frac{7}{2}$

Next, you would substitute the given points and the slope that you found into the point-slope formula:

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$