### All GMAT Math Resources

## Example Questions

### Example Question #41 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 #42 : Coordinate Geometry

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

**Possible Answers:**

None of the answers are correct.

**Correct answer:**

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 #43 : Coordinate Geometry

Given:

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

**Possible Answers:**

**Correct answer:**

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 #44 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 #45 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 #46 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 #47 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 .