# How do you write the equation of a line passing through (-5, 2) and parallel to the line whose equation is y=-4x +3?

Apr 25, 2018

$y = - 4 x + 10$

#### Explanation:

We know that the slope of the line is 4 units down for every 1 unit to the right, and that the line intercepts the y axis at 3. A parallel line will have a different y intercept but the same slope, so we already know that the equation must be $y = - 4 x + b$, with b as the y intercept.

We also know that the line passes through point (-5,2). We can thus substitute x and y for -5 and 2 respectively, to find b.

$2 = \left(- 4 \cdot 2\right) + b$

Simplify the equation
$2 = - 8 + b$

$10 = b$
$b = 10$

$y = - 4 x + 10$