# How do you find the equation of the line that passes through the x intercept of the line 5x-7y+45=0 and is perpendicular to the line y=2/5x-3?

Nov 30, 2016

The given line $y = \frac{2}{5} x - 3$ has a slope, $m = \frac{2}{5}$

The slope, n, of a perpendicular line is:

$n = - \frac{1}{m}$

$n = - \frac{5}{2}$

Therefore, a line that is perpendicular to the line $y = \frac{2}{5} x - 3$ will be of the form:

$y = - \frac{5}{2} x + b$

To find the x intercept of the line $5 x - 7 y + 45 = 0$, substitute 0 for y and the solve for x:

$5 x + 45 = 0$

$x = - 9$

Use the point $\left(- 9 , 0\right)$, to find the value of b:

$0 = - \frac{5}{2} \left(- 9\right) + b$

$b = - \frac{45}{2}$

The equation of the desired line is:

$y = - \frac{5}{2} x - \frac{45}{2}$