# Thread: Find Equation of Parallel and Perpendicular Lines

1. ## Find Equation of Parallel and Perpendicular Lines

Find an equation of the following parallel and perpendicular lines.

A.) The line parallel to $\displaystyle x+3=0$ and passing through $\displaystyle (-6, -7)$

B.) The line perpendicular to $\displaystyle y-4=0$ passing through $\displaystyle (-1, 6)$

Is there a specific formula I can use to to solve these?

2. Originally Posted by larry21
Find an equation of the following parallel and perpendicular lines.

A.) The line parallel to $\displaystyle x+3=0$ and passing through $\displaystyle (-6, -7)$

B.) The line perpendicular to $\displaystyle y-4=0$ passing through $\displaystyle (-1, 6)$

Is there a specific formula I can use to to solve these?

The equation of a line passing through a point $\displaystyle (x_1, y_1)$ is given by:

$\displaystyle y-y_1 = m(x-x_1)$

where m is the slope.

Now, two lines are parallel if their slopes are equal.

and two lines are perpendicular if the product of their slopes is -1.

3. Originally Posted by harish21
$\displaystyle y-y_1 = m(x-x_1)$
For reference, this equation is known as the point-slope equation.

4. 1)required line is parallel to x+3=0 and passes through (-6,-7)
equation of such line will be x=c. since it passes through (-6,-7)
-6=c or
x=-6
x+6=0
[NOTE: line x+k=0 is perpendicular to x axis so any line parallel to it must also be perpendicular to x axis and in the form x+k=0]

2) line perpendicular to y-4=0 will be in the form x=c.
since it passes through(-1,6)
we have -1=c
or c=-1
x=-1
x+1=0