# How do you find a standard form equation for the line Perpendicular to the line 7x+y=49; contains the point (7,-1)?

##### 1 Answer
Jun 12, 2016

$7 y - x = - 14$

#### Explanation:

Given lines $L$ and $L '$ which are perpendicular with each other,
their respective slopes $m$ and $m '$ have the following relation:

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

In the given equation, we have

$7 x + y = 49$

Transform the equation to slope-intercept form to get the slope.

$\implies y = - 7 x + 49$

$\implies m = - 7$

$\implies m ' = - \frac{1}{-} 7$

$\implies m ' = \frac{1}{7}$

Now, the equation of the perpendicular line will be something like

$y = \frac{1}{7} x + b$

To get the y-intercept, simply substitute the coordinates of the point which we know to lie on the line

$\implies - 1 = \frac{1}{7} \left(7\right) + b$

$\implies - 1 = 1 + b$

$\implies b = - 2$

Hence, the equation of the perpendicular line is

$y = \frac{1}{7} x - 2$

or, in standard form

$7 y = x - 14$

$\implies 7 y - x = - 14$