# How do you find the equation of the line through the points (4,5) that is perpendicular to the line 3x-4y=7?

Jun 11, 2016

The important fact about perpendicular lines is that the slope of a line perpendicular to one line is the negative reciprocal of slope of the initial line.

#### Explanation:

Let's first convert to slope intercept form, $y = m x + b$. This can be done by isolating $y$.

$3 x - 4 y = 7$

$- 4 y + 7 - 3 x$

$y = - \frac{7}{4} + \frac{3}{4} x$

$\therefore$ The slope of this line is $\frac{3}{4}$. Therefore, the slope of the line perpendicular will be $- \frac{4}{3}$.

Now, by point slope form we have:

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

$y - 5 = - \frac{4}{3} \left(x - 4\right)$

$y - 5 = - \frac{4}{3} x + \frac{16}{3}$

$y = - \frac{4}{3} x + \frac{31}{3}$

Hopefully this helps!