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Parallel and Perpendicular Line Calculator

Find parallel and perpendicular lines step by step

The calculator will find the equation of the parallel/perpendicular line to the given line passing through the given point, with steps shown.

For drawing lines, use the graphing calculator.

Find the equation of the line to the line passing through the point (, )

Enter the equation of a line in any form: y=2x+5, x-3y+7=0, etc.
If you need to find a line given two points or a slope and one point, use line calculator.
To find a slope, use slope calculator.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Solution

Your input: find the equation of the line perpendicular to the line $$$y=- 4 x - 1$$$ passing through the point $$$\left(-2,2\right)$$$.

The equation of the line in the slope-intercept form is $$$y=- 4 x - 1$$$.

The slope of the perpendicular line is negative inverse: $$$m=\frac{1}{4}$$$.

So, the equation of the perpendicular line is $$$y=\frac{x}{4}+a$$$.

To find $$$a$$$, we use the fact that the line should pass through the given point: $$$2=\left(\frac{1}{4}\right) \cdot \left(-2\right)+a$$$.

Thus, $$$a=\frac{5}{2}$$$.

Therefore, the equation of the line is $$$y=\frac{x}{4} + \frac{5}{2}$$$.

Answer: $$$y=\frac{x}{4} + \frac{5}{2}$$$.