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

Dec 6, 2015

$y = \frac{1}{2} x - 12$

#### Explanation:

Perpendicular lines have opposite reciprocal slopes.

The slope of the line $y = - 2 x + 5$ is $- 2$.

The opposite reciprocal of $- 2$ is $\frac{1}{2}$, which is the slope of the perpendicular line.

We also know that the line passes through the point $\left(4 , - 10\right)$.

We can use the $y = m x + b$ form of the line to determine the equation.

We know that:
$x = 4$
$y = - 10$
$m = \frac{1}{2}$
And we want to solve for $b$.

$- 10 = \frac{1}{2} \left(4\right) + b$

$- 10 = 2 + b$

$- 12 = b$

The equation of the line is $y = \frac{1}{2} x - 12$.