# 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.

### Solution

**Your input: find the equation of the line parallel to the line $$$y=2 x + 5$$$ passing through the point $$$\left(-3,5\right)$$$.**

The equation of the line in the slope-intercept form is $$$y=2 x + 5$$$.

The slope of the parallel line is the same: $$$m=2$$$.

So, the equation of the parallel line is $$$y=2 x+a$$$.

To find $$$a$$$, we use the fact that the line should pass through the given point: $$$5=\left(2\right) \cdot \left(-3\right)+a$$$.

Thus, $$$a=11$$$.

Therefore, the equation of the line is $$$y=2 x + 11$$$.

**Answer: $$$y=2 x + 11$$$.**