# How do you write an equation of a line Perpendicular to 3x+4y=12, through (7, 1)?

Nov 14, 2016

$4 x - 3 y - 25 = 0$

#### Explanation:

Product of the slopes of two lines perpendicular to each other is $- 1$. Let the slope of desired line be $m$.

Writing the equation of given line $3 x + 4 y = 12$ in slope intercept form, we get

$4 y = - 3 x + 12$ or $y = - \frac{3}{4} x + 3$

Hence slope of this line is $- \frac{3}{4}$.

As such we have $\frac{- 3}{4} \times m = - 1$

or $m = - 1 \times \frac{4}{- 3} = \frac{4}{3}$

Hence, slope of desired line is $\frac{4}{3}$ and as it passes through $\left(7 , 1\right)$

we can have equation of desired line using point slope form of equation i.e.

$\left(y - 1\right) = \frac{4}{3} \left(x - 7\right)$

or 3((y-1)=4(x-7)

or $3 y - 3 = 4 x - 28$

or $4 x - 3 y - 25 = 0$
graph{(3x+4y-12)(4x-3y-25)=0 [-6.21, 13.79, -3.32, 6.68]}