# How do you write an equation of a line passing through (-4, -3), perpendicular to 4x + y=7?

Sep 4, 2016

The equation is $y = \frac{1}{4} x - 2$.

#### Explanation:

A line perpendicular to another will have a slope that's the negative reciprocal of the other.

Let's make the initial equation into slope-intercept form$\to y = m x + b$

$4 x + y = 7 \to y = 7 - 4 x$

The slope here is $- 4$.

The slope of the line perpendicular will be $\frac{1}{4}$.

By point-slope form, the equation of the line perpendicular is:

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

$y - \left(- 3\right) = \frac{1}{4} \left(x - \left(- 4\right)\right)$

$y + 3 = \frac{1}{4} x + 1$

$y = \frac{1}{4} x - 2$

Hopefully this helps!