# How do you write an equation for the line in slope intercept form that is perpendicular to the given line and that passes through the given point –4x + 12y = 18; (–2, 4)?

$y = - 3 x - 2$

#### Explanation:

The slope of straight line $- 4 x + 12 y = 18$ or $y = \frac{1}{3} x + \frac{9}{2}$ is
$\frac{1}{3}$

The unknown line is perpendicular to the given line: $- 4 x + 12 y = 18$ hence, the slope of unknown line

$= - \frac{1}{\frac{1}{3}} = - 3$

Now, the equation of line with a slope $m = - 3$ passing through the point $\left(- 2 , 4\right) \setminus \equiv \left({x}_{1} , {y}_{1}\right)$ is given as follows

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

$y - 4 = - 3 \left(x - \left(- 2\right)\right)$

$y = - 3 x - 2$

Above is the slope intercept form of line