IXL - Equations of parallel and perpendicular lines (Geometry practice)

Line

has an equation of

–

Parallel to line

is line

which passes through the point

(

)

What is the equation of line

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Learn with an example

question

The equation of line

–

Line

includes the point

(

–

)

and is perpendicular to line

What is the equation of line

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

key idea

Perpendicular lines have slopes that are opposite reciprocals, like

and

–

Opposite reciprocals have a product of

–

The slope-intercept form of a linear equation is

where

is the slope and

is the

-intercept.

solution

Step 1: Find the slope of line

First find the slope

of line

This is the only time you will use the equation of line

–

Line

has a slope

–

Step 2: Find the slope of line

Line

is perpendicular to

so its slope is the opposite reciprocal:

Step 3: Use the slope of line

and a point on line

to find its

-intercept.

Plug the slope

and the point

(

–

)

into the slope-intercept formula. Then solve for the

-intercept

–

Plug in

–

and

(

)

Plug in

–

and

–

Multiply and simplify

–

Subtract

from both sides

Subtract

from both sides

–

Rewrite with a common denominator

–

Subtract

Line

has a

-intercept

–

Step 4: Use the slope of line

and the

-intercept

of line

to find the equation of the line.

Plug the slope

and the

-intercept

–

into the slope-intercept formula.

Plug in

and

–

Plug in

and

–

Rewrite as subtraction

–

Rewrite as subtraction

The equation of line

in slope-intercept form is

–

Looking for more? Try these:

Lesson: Equations of parallel and perpendicular lines

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Teacher tools

Work it out

Not feeling ready yet? These can help:

E.4Slopes of parallel and perpendicular lines

E.3Equations of lines

Lesson: Equations of parallel and perpendicular lines

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