# How do you write the equation of line passes through (-4,-3), and is perpendicular to 4x + y=7?

Feb 1, 2017

$3 x - y + 14 = 0$

#### Explanation:

Equation of a line that is perpendicular to $A x + B y = C$

is of the form $B x - A y = k$ i.e. reversing te coefficients of $x$ and $y$ and changing sign of one of them.

Hence, the line perpendicular to $4 x + y = 7$ has equation of the form

$x - 4 y = k$ and as it passes through $\left(- 4 , - 3\right)$

we should have $\left(- 4\right) - 4 \times \left(- 3\right) = k$

and therefore $k = - 4 + 12 = 8$

and desired equation is $x - 4 y = 8$ or $3 x - y + 14 = 0$
graph{(x-4y-8)(4x+y-7)=0 [-10, 10, -5, 5]}