# What is the equation of a line that satisfies the given conditions: perpendicular to y= -2x + 5 and passing through (4, -10)?

Nov 19, 2015

$y = 0.5 x - 12$

#### Explanation:

Since the line must be perpendicular, the slope $m$ should be the opposite and inverse of the one in your original function.

$m = - \left(- \frac{1}{2}\right) = \frac{1}{2} = 0.5$

Now all you have to do is use the point slope equation:

Given coordinate: $\left(4 , - 10\right)$

$y - {y}_{0} = m \left(x - {x}_{0}\right)$

$y - \left(- 10\right) = 0.5 \left(x - 4\right)$

$y + 10 = 0.5 x - 2$

$y = 0.5 x - 2 - 10$

$y = 0.5 x - 12$