# What is the equation of the line perpendicular to y=-5/9x  that passes through  (-7,3) ?

Jan 16, 2016

5y - 9x + 48 = 0

#### Explanation:

One of the forms of the equation of a straight line is y = mx + c where m represents the gradient and c , the y-intercept.

the line $y = - \frac{5}{9} x$

is in this form with c = 0 and m = $- \frac{5}{9}$

When 2 lines are perpendicular then the product of their gradients :

${m}_{1} {m}_{2} = - 1$

The gradient of the perpendicular line is : $- \frac{5}{9} \times {m}_{2} = - 1$

$\Rightarrow {m}_{2} = - \frac{1}{- \frac{5}{9}} = \frac{9}{5}$

equation : y - b = m(x - a ) , m = $\frac{9}{5} , \left(a , b\right) = \left(- 7 , 3\right)$

$\Rightarrow y - 3 = \frac{9}{5} \left(x - 7\right)$

multiply both sides by 5 to eliminate fraction : $5 y - 15 = 9 x - 63$

equation of perpendicular line is 5y - 9x + 48 = 0