SSAT Upper Level Math : How to find the equation of a parallel line

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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

Which of the following equations gives a line that is parallel to the line with the equation ?

Possible Answers:

Correct answer:

Explanation:

Two lines are parallel when they have the same slope. Because the slope of the given line is , the slope to a line parallel to it must also be . The only answer choice that has a slope of  is , so it is the correct answer.

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

A line has the equation . If a second line goes through the point  and is parallel to the first line, what is the equation of this second line?

Possible Answers:

Correct answer:

Explanation:

The slope of the second line must be  if these two lines are to be parallel.

To find the equation of this second line, just plug in the given point into the standard form  equation to find its -intercept.

Now we have all the parts needed to write the equation for the second line:

Example Question #3 : How To Find The Equation Of A Parallel Line

Line  is parallel to line  and goes through the point . The equation for line  is . Find the equation of line .

Possible Answers:

Correct answer:

Explanation:

Since lines  and  are parallel, the slope of line  must also be . Now, plug the given point into the equation  to find the -intercept of line :

Thus, the equation of line  is 

Example Question #1 : Parallel Lines

There is a line defined by the equation below:

There is a second line that passes through the point  and is parallel to the line given above. What is the equation of this second line?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = 3x + 12

y = (3/4)x + 3

slope = 3/4

We know that the second line will also have a slope of 3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = 3/4(1) + b

2 = 3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = (3/4)x + 2.75

Example Question #3 : Coordinate Geometry

What is the equation of a line that is parallel to  and passes through ?

Possible Answers:

Correct answer:

Explanation:

To solve, we will need to find the slope of the line. We know that it is parallel to the line given by the equation, meaning that the two lines will have equal slopes. Find the slope of the given line by converting the equation to slope-intercept form.

The slope of the line will be . In slope intercept-form, we know that the line will be . Now we can use the given point to find the y-intercept.

The final equation for the line will be .

Example Question #4 : Coordinate Geometry

What line is parallel to   and passes through the point ?

Possible Answers:

Correct answer:

Explanation:

Start by converting the original equation to slop-intercept form.

The slope of this line is . A parallel line will have the same slope. Now that we know the slope of our new line, we can use slope-intercept form and the given point to solve for the y-intercept.

Plug the y-intercept into the slope-intercept equation to get the final answer.

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 #2 : How To Find The Equation Of Parallel Lines

What line is parallel to , and passes through the point ?

Possible Answers:

Correct answer:

Explanation:

Converting the given line to slope-intercept form we get the following equation:

For parallel lines, the slopes must be equal, so the slope of the new line must also be . We can plug the new slope and the given point into the slope-intercept form to solve for the y-intercept of the new line.

Use the y-intercept in the slope-intercept equation to find the final answer.

Example Question #11 : Coordinate Geometry

What line is parallel to  at ?

Possible Answers:

None of the answers are correct

Correct answer:

Explanation:

Find the slope of the given line:  (slope intercept form)

 therefore the slope is 

Parallel lines have the same slope, so now we need to find the equation of a line with slope  and going through point  by substituting values into the point-slope formula.

So, 

Thus, the new equation is 

Example Question #1 : Parallel Lines

If the line through the points (5, –3) and (–2, p) is parallel to the line y = –2x – 3, what is the value of p ?

Possible Answers:

17

11

0

4

10

Correct answer:

11

Explanation:

Since the lines are parallel, the slopes must be the same. Therefore, (p+3) divided by (25) must equal 2. 11 is the only choice that makes that equation true. This can be solved by setting up the equation and solving for p, or by plugging in the other answer choices for p. 

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