Write The Equation Of Perpendicular Line Worksheet

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Find the negative reciprocal of the original line's slope in order to obtain the equation of a perpendicular line to a given line. The perpendicular line will have a slope of `-\frac{1}{m}` if the slope of the original line is $ m $. Next, substitute the slope and a point where the perpendicular line passes in the point-slope form of a line equation $ y - y_1 = m(x - x_1) $.

Algebra 1

Linear Relationship

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.

How to Write the Equation of Perpendicular Line?

Determine the equation of the given line in

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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 = $-\frac{1}{2}x - \frac{1}{2}$

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