# SSAT Upper Level Math : Parallel Lines

## Example Questions

### Example Question #5 : How To Find The Slope Of Parallel Lines

What is the slope of the line ?

Explanation:

In order to most easily determine the slope, let's turn this equation into its slope-intercept form :

We can start by subtracting  from each side in order to isolate  on one side of the equation:

Then, we can divide the entire equation by :

, or

Therefore, .

### 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 ?

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 #2 : 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?

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 .

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 : How To Find The Equation Of A Parallel Line

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?

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 #1 : Coordinate Geometry

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

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

What line is parallel to   and passes through the point ?

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 #4 : How To Find The Equation Of A Parallel Line

What is the equation of a line that is parallel to the line and includes the point ?

Explanation:

The line parallel to must have a slope of , giving us the equation . To solve for b, we can substitute the values for y and x.

Therefore, the equation of the line is .

### Example Question #5 : How To Find The Equation Of A Parallel Line

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

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 #6 : How To Find The Equation Of A Parallel Line

What line is parallel to  at ?

None of the answers are correct