How do you write the equation in point slope form given (-4,-3), perpendicular to 4x + y=7 ?

Dec 24, 2016

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

Explanation:

First, we must solve for $y$.
For this, we just need to subtract $4 x$ from both sides of the equation. Once we do this we should get:
$y = - 4 x + 7$

Any question that asks you for a line (or equation) perpendicular to another, you should know that the slope of the new line will be the negative reciprocal of the slope given.

In your case the opposite of $- 4 x$ is $- \frac{1}{4} x$ and then we need to multiply this by a negative, to get $\frac{1}{4} x$

From here, you have enough information to solve the problem using point slope form. Which is:
$y - y 1 = m \left(x - x 1\right)$

Now we plug in what we are given: $y 1$ is -3 (from the point given in the question), $m$ is our new slope, $\frac{1}{4} x$ and $x 1$ is -4 (from the point given in the question)

Our equation should now be $y + 3 = \frac{1}{4} \left(x + 4\right)$
This is the complete equation in point slope form (as asked for in the question). If you, or others reading this, want to simplify further to slope intercept form which is $y = m x + b$ see notes below.

To continue, we distribute $\frac{1}{4} \left(x + 4\right)$ to get $\frac{1}{4} x + 1$

our equation is now $y + 3 = \frac{1}{4} x + 1$

our final step is to subtract 3 from both sides, to get $y = \frac{1}{4} x - 2$