# If L is a line perpendicular to the line y + 4x= 5 and passes through the point (2,4), what is the x intercept of L?

x-intercept $= - 14$

#### Explanation:

The slope of $y + 4 x = 5$ is $m = - 4$

A line L perpendicular to it has a slope ${m}_{p} = - \left(\frac{1}{- 4}\right) = \frac{1}{4}$

The equation of the line passing thru $\left(2 , 4\right)$ with slope ${m}_{p} = \frac{1}{4}$

$y - 4 = \frac{1}{4} \left(x - 2\right)$

$y = \frac{1}{4} x - \frac{2}{4} + 4$

$y = \frac{1}{4} x + \frac{7}{2}$

Set $y = 0$ the solve for the x-intercept

$y = \frac{1}{4} x + \frac{7}{2}$

$0 = \frac{1}{4} x + \frac{7}{2}$

$\frac{1}{4} x = - \frac{7}{2}$

$x = - 14$

God bless...I hope the explanation is useful.