SAT Math : How to find the equation of a parallel line

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #7 : How To Find The Equation Of A Parallel Line

Which of these formulas could be a formula for a line perpendicular to the line ?

Possible Answers:

Correct answer:


This is a two-step problem. First, the slope of the original line needs to be found. The slope will be represented by "" when the line is in -intercept form .

So the slope of the original line is . A line with perpendicular slope will have a slope that is the inverse reciprocal of the original. So in this case, the slope would be . The second step is finding which line will give you that slope. For the correct answer, we find the following:

So, the slope is , and this line is perpendicular to the original.

Example Question #11 : Lines

Which of the following equations is parallel to:  and goes through the point ?

Possible Answers:

Correct answer:


Step 1: We need to define what a parallel line is. A parallel line has the same slope as the line given in the problem. Parallel lines never intersect, which tells us that the y-intercepts of the two equations are different.

Step 2: We need to identify the slope of the line given to us. The slope is always located in front of the .

The slope in the equation is .

Step 3: If we said that a parallel line has the same slope as the given line in the equation, the slope of the parallel equation is also .

Step 4. We need to write the equation of the parallel line in slope-intercept form:. We need to write b for the intercept because it has changed.

The equation is: 

Step 5: We will use the point  where  and . We need to substitute these values of x and y into the equation in step 4 and find the value of b.

The numbers in red will cancel out when I multiply.

To find b, subtract 2 to the other side

Step 6: We put all of the parts together and make the final equation of the parallel line:

The final equation is: 

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