# How do you write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the equation given (4, -5), 2x-5y= -10?

May 27, 2015

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

$2 x - 5 y = 10$

$5 y = 2 x - 10$

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

So $m = \frac{2}{5}$

For perpendicular lines: $m m ' = - 1$

So $m ' = - \frac{5}{2}$

$y = m ' x + c$

So:

$- 5 = \left(- \frac{5}{2}\right) \times 4 + c$

$c = - 5 + 10 = 5$

So:

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