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Algebra 1 : How to find the equation of a perpendicular line

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Example Question #91 : Perpendicular Lines

Suppose a line has an x-intercept of one and a y-intercept of two. What is the equation of the perpendicular line which pass through the point (9,8) ?

Possible Answers:

$y=\frac{1}{2}x+9$

$y=-\frac{1}{2}x-36$

$y=-\frac{1}{2}x+\frac{25}{2}$

$y=\frac{1}{2}x+\frac{7}{2}$

y=-2x+26

Correct answer:

$y=\frac{1}{2}x+\frac{7}{2}$

Explanation:

Write the points that correspond to the x and y-intercepts given in the problem.

X-intercept of one: (1,0)

Y-intercept of two: (0,2)

Find the slope of this line connected with these points.

$m=\frac{y_2-y_1}{x_2-x_1} = \frac{2-0}{0-1} = \frac{2}{-1} = -2$

The slope is negative two. The slope of the perpendicular line is the negative reciprocal of this slope.

$m_\textup{perpendicular} = -\frac{1}{m} = -\frac{1}{-2} = \frac{1}{2}$

Write the slope-intercept form.

y=mx+b

Substitute the perpendicular slope with the point that this line will pass through.

$8=(\frac{1}{2})(9)+b$

Solve for the y-intercept, .

$8=\frac{9}{2}+b$

Subtract nine halves on both sides.

$8-\frac{9}{2}=\frac{9}{2}+b-\frac{9}{2}$

Simplify both sides.

$\frac{16}{2}-\frac{9}{2} =b$

$b=\frac{7}{2}$

With the perpendicular slope and the y-intercept, write the equation of the line.

The answer is: $y=\frac{1}{2}x+\frac{7}{2}$

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Example Question #331 : Functions And Lines

What is the slope of a line perpendicular to the line with the following equation?

$3y+5x=9$

Possible Answers:

$\frac{5}{3}$

Answer cannot be determined from this information.

$-\frac{5}{3}$

$\frac{3}{5}$

$-\frac{3}{5}$

Correct answer:

$\frac{3}{5}$

Explanation:

Step 1: get the line into y = mx +b format to find the slope m:

$\\3x+5y=9\rightarrow \\\\ 3y=-5x+9\rightarrow\\\\ y=-\frac{5}{3}x+3$

Next, we need to remember that perpendicular lines have slopes that are negative reciprocals. Find the negative reciprocal of $-\frac{5}{3}$ :

$\frac{3}{5}$

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Algebra 1 : How to find the equation of a perpendicular line

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #91 : Perpendicular Lines

Example Question #331 : Functions And Lines

All Algebra 1 Resources

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