How do you write an equation of a line, given (4,5) that is perpendicular to the line 3x-4y=7?

Jun 30, 2017

$4 x + 3 y = 31$

Explanation:

Rearrange the original equation into form: $y = m x + c$

$\left(y = \frac{3}{4} x - \frac{7}{4}\right) .$

The perpendicular gradient is the negative reciprocal of $\frac{3}{4}$
(just change the sign and flip the fraction upside down)
which is $- \frac{4}{3}$.

Now use $y - {y}_{1} = m \left(x - {x}_{1}\right) ,$ substituting the $4 \mathmr{and} 5$.

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

Rearrange the resulting equation (usually asked for in integer form)

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

$3 y - 15 = - 4 x + 16$

$4 x + 3 y = 31$