# GMAT Math : Calculating the equation of a parallel line

## Example Questions

### Example Question #642 : Geometry

What is the equation of the line that is parallel to and goes through point ?

Explanation:

Parallel lines have the same slope. Therefore, the slope of the new line is , as the equation of the original line is  ,with slope .

and      :

### Example Question #14 : Parallel Lines

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

None of the answers are correct.

Explanation:

The parallel line has the equation . We can find the slope by putting the equation into slope-intercept form, y = mx + b, where m is the slope and b is the intercept.   becomes , so the slope is 2.

We know that our line must have an equation that looks like . Now we need the intercept. We can solve for b by plugging in the point (4, 1).

1 = 2(4) + b

b = –7

Then the line in question is .

### Example Question #643 : Geometry

Given:

Which of the following is the equation of a line parallel to  that has a y-intercept of ?

Explanation:

Parallel lines have the same slope, so our slope will still be 4. The y-intercept is just the "+b" at the end. In f(x) the y-intercept is 13. In this case, we need to have a y-intercept of -13, so our equation just becomes:

### Example Question #644 : Geometry

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

Explanation:

Two lines are parallel if they have the same slope. The slope of g(x) is 6, so eliminate anything without a slope of 6.

Recall slope intercept form which is .

We know that the line must have an m of 6 and an (x,y) of (8,9). Plug everything in and go from there.

So we get:

### Example Question #17 : Parallel Lines

Given the function , which of the following is the equation of a line parallel to  and has a -intercept of ?

Explanation:

Given a line  defined by the equation  with slope , any line that is parallel to  also has a slope of . Since , the slope  is  and the slope of any line  parallel to  also has a slope of .

Since  also needs to have a -intercept of , then the equation for  must be

### Example Question #18 : Parallel Lines

Given the function , which of the following is the equation of a line parallel to  and has a -intercept of ?

Explanation:

Given a line  defined by the equation  with slope , any line that is parallel to  also has a slope of . Since , the slope  is  and the slope of any line  parallel to  also has a slope of .

Since  also needs to have a -intercept of , then the equation for  must be

### Example Question #19 : Parallel Lines

Given the function , which of the following is the equation of a line parallel to  and has a -intercept of ?