### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Find The Slope Of Parallel Lines

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

**Possible Answers:**

**Correct answer:**

For two lines to be parallel, their slopes must be the same. Since the slope of the given line is , the line that is parallel to it must also have a slope of .

### Example Question #2 : How To Find The Slope Of Parallel Lines

Line has the equation . If line is parallel to line , what is the slope of line ?

**Possible Answers:**

**Correct answer:**

Line must have the same slope as line to be parallel with it, so the slope of line must be . You can tell that the slope of line is because it is in form, and the value of is the slope.

### Example Question #1 : How To Find The Slope Of Parallel Lines

What is the slope of a line parallel to the line: -15x + 5y = 30 ?

**Possible Answers:**

1/3

30

3

-15

**Correct answer:**

3

First, put the equation in slope-intercept form: y = 3x + 6. From there we can see the slope of this line is 3 and since the slope of any line parallel to another line is the same, the slope will also be 3.

### Example Question #11 : Lines

What is the slope of any line parallel to –6x + 5y = 12?

**Possible Answers:**

5/6

12/5

6/5

12

6

**Correct answer:**

6/5

This problem requires an understanding of the makeup of an equation of a line. This problem gives an equation of a line in y = mx + b form, but we will need to algebraically manipulate the equation to determine its slope. Once we have determined the slope of the line given we can determine the slope of any line parallel to it, becasue parallel lines have identical slopes. By dividing both sides of the equation by 5, we are able to obtain an equation for this line that is in a more recognizable y = mx + b form. The equation of the line then becomes y = 6/5x + 12/5, we can see that the slope of this line is 6/5.

### Example Question #2 : How To Find The Slope Of Parallel Lines

What is the slope of a line that is parallel to the line 11x + 4y - 2 = 9 – 4x ?

**Possible Answers:**

**Correct answer:**

We rearrange the line to express it in slope intercept form.

Any line parallel to this original line will have the same slope.

### Example Question #11 : Coordinate Geometry

In the standard (x, y) coordinate plane, what is the slope of a line parallel to the line with equation ?

**Possible Answers:**

**Correct answer:**

Parallel lines will have equal slopes. To solve, we simply need to rearrange the given equation into slope-intercept form to find its slope.

The slope of the given line is . Any lines that run parallel to the given line will also have a slope of .

### Example Question #1 : How To Find The Slope Of Parallel Lines

What is the slope of a line that is parallel to the line ?

**Possible Answers:**

**Correct answer:**

Parallel lines have the same slope. The question requires you to find the slope of the given function. The best way to do this is to put the equation in slope-intercept form (y = mx + b) by solving for y.

First subtract 6x on both sides to get 3y = –6x + 12.

Then divide each term by 3 to get y = –2x + 4.

In the form y = mx + b, m represents the slope. So the coefficient of the x term is the slope, and –2 is the correct answer.

### Example Question #3 : How To Find The Slope Of Parallel Lines

Line is defined by the equation . If Line is parallel to Line , what is the slope of Line ?

**Possible Answers:**

**Correct answer:**

Any line that is parallel to a line must have the same slope . Since Line has a slope , Line must also have a slope .

### Example Question #1 : How To Find The Slope Of Parallel Lines

Which of the following is a line that is parallel to the line ?

**Possible Answers:**

**Correct answer:**

For a given line , a parallel line must have the same slope . Given the answer choices above, only has the same slope .

### Example Question #1 : How To Find The Slope Of Parallel Lines

What is the slope of the line ?

**Possible Answers:**

**Correct answer:**

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, .

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