Intermediate Geometry : How to find the equation of a parallel line

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #2 : Lines

What is the equation of a line that is parallel to the line \small y=\frac{1}{2}x+3 and includes the point ?

Possible Answers:

\small y=-2x+10

\small y=2x-6

\small y=\frac{1}{2}x

\small y=\frac{1}{2}x+6

Correct answer:

\small y=\frac{1}{2}x

Explanation:

The line parallel to \small y=\frac{1}{2}x+3 must have a slope of \frac{1}{2}, giving us the equation \small y=\frac{1}{2}x+b. To solve for b, we can substitute the values for y and x.

\small 2=(\frac{1}{2})(4)+b 

\small 2=2+b

\small b=0

Therefore, the equation of the line is \small y=\frac{1}{2}x.

Example Question #1 : How To Find The Equation Of A Parallel Line

Suppose a line  . What is the equation of a parallel line that intersects point ?

Possible Answers:

Correct answer:

Explanation:

A line parallel to  must have a slope of two. Given the point  and the slope, use the slope-intercept formula to determine the -intercept by plugging in the values of the point and solving for :

Plug the slope and the -intercept into the slope-intercept formula:

Example Question #31 : Parallel Lines

Find the equation of the line parallel to  that passes through the point .

Possible Answers:

Correct answer:

Explanation:

Write  in slope intercept form, , to determine the slope, :

The slope is:

Given the slope, use the point  and the equation  to solve for the value of the -intercept, . Substitute the known values.

With the known slope and the -intercept, plug both values back to the slope intercept formula. The answer is .

Example Question #32 : Parallel Lines

Given , find the equation of a line parallel.

Possible Answers:

Correct answer:

Explanation:

The definition of a parallel line is that the lines have the same slopes, but different intercepts. The only answer with the same slope is .

Example Question #33 : Parallel Lines

Which one of these equations is parallel to:

Possible Answers:

Correct answer:

Explanation:

Equations that are parallel have the same slope.

For the equation:

The slope is  since that is how much  changes with increment of .

The only other equation with a slope of  is:

Example Question #34 : Parallel Lines

What equation is parallel to:

Possible Answers:

Correct answer:

Explanation:

To find a parallel line to

we need to find another equation with the same slope of  or .

The only equation that satisfies this is .

Example Question #2 : How To Find The Equation Of A Parallel Line

What equation is parallel to:

Possible Answers:

Correct answer:

Explanation:

To find an equation that is parallel to

we need to find an equation with the same slope of .

 

Basically we are looking for another equation with .

The only other equation that satisfies this is

.

Example Question #36 : Parallel Lines

A line is parallel to the line of the equation 

and passes through the point .

Give the equation of the line in standard form.

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

Two parallel lines have the same slope. Therefore, it is necessary to find the slope of the line of the equation 

Rewrite the equation in slope-intercept form , the coefficient of , will be the slope of the line.

Add  to both sides:

Multiply both sides by , distributing on the right:

The slope of this line is . The slope of the first line will be the same. The slope-intercept form of the equation of this line will be 

.

To find , set  and  and solve:

Subtract  from both sides:

The slope-intercept form of the equation is 

To rewrite in standard form with integer coefficients:

Multiply both sides by 7:

Add  to both sides:

,

the correct equation in standard form.

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