This calculator find and plot equations of parallel and perpendicular to the given line and passes through given point. The calculator will generate a stepbystep explanation on how to obtain the result.

Equation of the line that passes through the point $A(x_0, y_0)$ and is parallel to the line $y = mx + b$ is:
$$ {\color{blue}{ y  y_0 = m(xx_0) }} $$Example:
Find the equation of the line that passes through the point $A(1, 2)$ and is parallel to the line $y = 2x  3$
Solution:
In this example we have: $ x_0 = 1,~~ y_0 = 2,~~ m = 2$. So we have:
$$ \begin{aligned} y  y_0 & = m(xx_0) \\ y  2 & = 2(x(1)) \\ y  2 & = 2x + 2 \\ y & = 2x + 2 + 2 \\ {\color{blue}{ y }} & {\color{blue}{ = 2x + 4}} \end{aligned} $$Note : If you want to solve this problem using above calculator, you need to rewrite line equation in general form ( $2x  y  3 = 0$ )
Equation of the line that passes through the point $A(x_0, y_0)$ and is perpendicular to the line $y = mx + b$ is:
$$ {\color{blue}{ y  y_0 = \frac{1}{m}(xx_0) }} $$Example:
Find the equation of the line that passes through the point $A(1, 2)$ and is perpendicular to the line $y = 2x  3$
Solution:
In this example we have: $ x_0 = 1,~~ y_0 = 2,~~ m = 2$. So we have:
$$ \begin{aligned} y  y_0 & = \frac{1}{m}(xx_0) \\ y  2 & = \frac{1}{2}(x(1)) \\ y  2 & = \frac{1}{2}(x + 1) \\ (y  2)\cdot{\color{red}{2}} & = \frac{1}{2}\cdot{\color{red}{2}}(x + 1) \\ 2(y  2) & = (x + 1)\\ 2y  4 & = x  1\\ 2y & = x + 3\\ {\color{blue}{ y }} & = {\color{blue}{\frac{1}{2}x + \frac{3}{2} }} \end{aligned} $$Note : If you want to solve this problem using above calculator, you need to rewrite line equation in general form ( $2x  y  3 = 0$ )
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