# What is the equation of the line perpendicular to y=-2/7x  that passes through  (-2,5) ?

Dec 30, 2015

$y - 5 = \frac{7}{2} \left(x + 2\right)$ Equation in point-slope form.
$y = \frac{7}{2} x + 12$ Equation of the line in slope-intercept form

#### Explanation:

To find the equation of the line perpendicular to the given line.

Step 1: Find the slope of the given line.

Step 2: Take the slope's negative reciprocal to find the slope of perpendicular.

Step 3: Use the given point and the slope use the Point-Slope form to find the equation of line.

Let us write our given line and go through the steps one by one.

$y = - \frac{2}{7} x$

Step 1: Finding the slope of $y = - \frac{2}{7} x$
This is of the form $y = m x + b$ where $m$ is the slope.

Slope of the given line is $- \frac{2}{7}$

Step 2: The slope of perpendicular is the negative reciprocal of the given slope.

$m = - \frac{1}{- \frac{2}{7}}$
$m = \frac{7}{2}$

Step 3: Use the slope $m = \frac{7}{2}$ and the point #(-2,5) to find the equation of the line in the Point-Slope form.

Equation of line in Point-slope form when slope $m$ and a point $\left({x}_{1} , {y}_{1}\right)$ is $y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - 5 = \frac{7}{2} \left(x + 2\right)$ Solution in point-slope form.

Simplifying we can get
$y - 5 = \frac{7}{2} x + 7$ using distributive propertly
$y = \frac{7}{2} x + 7 + 5$ adding $5$ both sides

$y = \frac{7}{2} x + 12$ Equation of the line in slope-intercept form