Write The Equation Of Perpendicular Line Worksheet

6 problems

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:
1. 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.
2. 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: $2$
3. Slope of Line $h$: Line $h$ is perpendicular to $g$.$\newline$Slope of line $g$: $2$$\newline$Find the slope of line $h$.$\newline$Opposite reciprocal of $2$ is $-\frac{1}{2}$.$\newline$Slope of line $h$: $-\frac{1}{2}$
4. Y-Intercept Calculation: For line $h$: $\newline$Slope ($m$): $-\frac{1}{2}$ $\newline$Point: $(-5, 2)$ $\newline$Plug these values in $y = mx + b$ and find the y-intercept.$\newline$$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$
5. 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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