How do you write an equation in slope-intercept form for a line that is parallel to the given line y = -1/4x + 9 and passes through the given point(-4, 4)?

Jun 13, 2018

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

Explanation:

Since the line

$y = - \frac{1}{4} x + 9$

is already in slope-intercept form, we know that the slope of the line is $- \frac{1}{4}$.

Two lines are parallel if they have the same slope, so our line will also have slope $- \frac{1}{4}$, which means that it has equation like

$y = - \frac{1}{4} x + q$

Let's impose the passage through $\left(- 4 , 4\right)$:

$4 = - \frac{1}{4} \cdot \left(- 4\right) + q \setminus \iff 4 = 1 + q \setminus \iff q = 3$

So, the equation is

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