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