ACT Math : How to find the equation of a perpendicular line

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #11 : How To Find The Equation Of A Perpendicular Line

Line  follows the equation .

State the equation, in slope-intercept form, of line , which is perpendicular to line  and intersects it at point .

Possible Answers:

Correct answer:

Explanation:

Since line  follows the equation , we can surmise its slope is . Thus, it follows that any line perpendicular to  will have a slope of .

Since we also know at least one point on line , we can use point slope form to find an initial equation for our line.

----> .

Next, we can simplify to reach point-slope form.

---->.

Thus, line  in slope-intercept form is .

Example Question #91 : Coordinate Geometry

Which of the following equations represents a line that goes through the point  and is perpendicular to the line  ?

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need first to transform the equation from standard form to slope-intercept form:

Transform the original equation to find its slope.

 

First, subtract  from both sides of the equation.

Simplify and rearrange.

 

Next, divide both sides of the equation by 6.

The slope of our first line is equal to . Perpendicular lines have slopes that are opposite reciprocals of each other; therefore, if the slope of one is x, then the slope of the other is equal to the following: 

Let's calculate the opposite reciprocal of our slope:

The slope of our line is equal to 2. We now have the following partial equation:

We are missing the y-intercept, . Substitute the x- and y-values in the given point  to solve for the missing y-intercept. 

 

Add 4 to both sides of the equation.

Substitute this value into our partial equation to construct the equation of our line:

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