Write The Equation Of Perpendicular Line Worksheets [PDF]: Algebra 1 Math

How Will This Worksheet on "Write the Equation of Perpendicular Line" Benefit Your Student's Learning?

Reinforces the concept that slopes of perpendicular lines are negative reciprocals.
Enhances problem-solving abilities by applying mathematical theory to practical issues.
Prepares students for advanced math classes like calculus and geometry.
Essential for professions requiring precise angles, such as engineering and architecture.
Encourages critical thinking and the study of geometric relationships.
Improves communication skills in expressing mathematical ideas clearly.
Builds confidence in solving challenging mathematical tasks.

Determine the equation of the given line in slope-intercept form `y = mx + c` or standard form `Ax + By = C`. If not given, find the slope `m` and a point `(x_1, y_1)` on the line.
Calculate the slope `m_{\perp}` of the perpendicular line, which is the negative reciprocal of the slope `m` of the given line. The negative reciprocal is `-\frac{1}{m}`.
Determine a point through which the perpendicular line passes, or the intersection point with the given line. Let this point be `(x_1, y_1)`.
Use the point-slope form of the equation of a line:
$ y - y_1 = m_{\perp}(x - x_1) $
If needed, convert the equation from point-slope form to standard form `Ax + By = C`.

Solved Example

Q. Line

g

has an equation of

y = 2x + 1

. Line

h

includes the point

(-5,2)

and is perpendicular to line

g

. What is the equation of line

h

\newline

Write the equation in slope-intercept form.

Solution:

Perpendicular Lines Slopes: Line $h$ is perpendicular to line $g$ . $\newline$ Are their slopes the same or opposite reciprocals? $\newline$ Slopes of perpendicular lines are opposite reciprocals.
Equation of Line g: Equation of line g: $\newline$ $y = 2x + 1$ $\newline$ Find the slope of line g. $\newline$ Compare $y = 2x + 1$ with $y = mx + b$ . $\newline$ $m = 2$ $\newline$ Slope of line g: $2$
Slope of Line $h$ : Line $h$ is perpendicular to $g$ . $\newline$ Slope of line $g$ : $2$ $\newline$ Find the slope of line $h$ . $\newline$ Opposite reciprocal of $2$ is $-\frac{1}{2}$ . $\newline$ Slope of line $h$ : $-\frac{1}{2}$
Y-Intercept Calculation: For line $h$ : $\newline$ Slope ( $m$ ): $-\frac{1}{2}$ $\newline$ Point: $(-5, 2)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $2 = -\frac{1}{2}(-5) + b$ $\newline$ $2 = \frac{5}{2} + b$ $\newline$ $2 - \frac{5}{2} = b$ $\newline$ $\frac{4}{2} - \frac{5}{2} = b$ $\newline$ $-\frac{1}{2} = b$
Equation of Line h: For line h: $\newline$ Slope $m$ : $-\frac{1}{2}$ $\newline$ y-intercept $b$ : $-\frac{1}{2}$ $\newline$ What is the equation of the line h in slope-intercept form? $\newline$ Substitute $-\frac{1}{2}$ for $m$ and $-\frac{1}{2}$ for $b$ in $y = mx + b$ . $\newline$ y = $-\frac{1}{2}x - \frac{1}{2}$