Math Problem Solver

Slope-Intercept Form:

Perpendicular lines are two lines in the same plane which intersect at a 90 degree angle. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the given line can be used to find the slope of a line perpendicular to it.$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned} y &= 2 x + 5 \\ \text{Slope} &= m = 2 \end{aligned}$$The negative reciprocal of $2$ is $- \frac{1}{2}$, therefore $m$ of a perpendicular line will be $- \frac{1}{2}$.$$\begin{aligned}y &= - \frac{1}{2}x+b \\ -1 &= - \frac{1}{2}(3)+b \\ b &= \frac{1}{2} \end{aligned}$$An equation of the line in slope-intercept form is: $y = - \frac{1}{2}x +\frac{1}{2}$.

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Point-Slope Form:

Perpendicular lines are two lines in the same plane which intersect at a 90 degree angle. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the given line can be used to find the slope of a line perpendicular to it.$$\begin{aligned} y &= 2 x + 5 \\ \text{Slope} &= m = 2 \end{aligned}$$The negative reciprocal of $2$ is $- \frac{1}{2}$, therefore $m$ of a perpendicular line will be $- \frac{1}{2}$.$$\begin{aligned} y - y_{1} = m(x - x_{1}) \end{aligned}$$$$ \text{where m } = - \frac{1}{2}, \text{ } x_{1} = 3, \text{ and } y_{1} = -1 $$An equation of the line in point-slope form is: $y + 1 = - \frac{x - 3}{2}$

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Standard Form:

Perpendicular lines are two lines in the same plane which intersect at a 90 degree angle. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the given line can be used to find the slope of a line perpendicular to it.$$\begin{aligned}Ax + By + C &= 0 \\ -2x +1y -5 &= 0 \end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ \text{Slope} &= 2 \end{aligned}$$The negative reciprocal of $2$ is $- \frac{1}{2}$, therefore $A$ and $B$ of a perpendicular line are $1$ and $2$.$$\begin{aligned} 1x +2y + C &= 0 \\ 1(3) +2(-1)+C &= 0 \\ 3 + C &= 2 \\ C &= -1 \end{aligned}$$An equation of the line in standard form is: $1x +2y -1 = 0$