### All SAT Math Resources

## Example Questions

### Example Question #101 : Lines

Consider line c to be y= -4x - 7. Which is the reflection of line c across the x-axis?

**Possible Answers:**

y = 4x – 7

y = –4x + 7

y = 4x + 7

y = (1/4)x + 7

**Correct answer:**

y = 4x + 7

A line reflected across the x-axis will have the negative value of the slope and intercept. This leaves y= 4x + 7.

### Example Question #1 : Parallel Lines

If line J passes through the points (1, 3) and (2, 4) and line K passes through (0, x) and (10, 3), what would be the value of x in order for lines J and K to be parallel?

**Possible Answers:**

–13

13

1

7

–7

**Correct answer:**

–7

Find the slope of line J, (4 – 3)/(2 – 1) = 1

Now use this slope in for the equation of line K of the form y = mx + b for the other point (10, 3)

3 = 10 + b → b = –7

So for the point (0, X) → X = 0 – 7,

so x = –7 when these two lines are parallel.

### Example Question #102 : Lines

Line is represented by the equation .

If line passes through the points and , and if is parallel to , then what is the value of ?

**Possible Answers:**

**Correct answer:**

We are told that lines *l* and *m* are parallel. This means that the slope of line *m* must be the same as the slope of *l*. Line *l* is written in the standard form of Ax + By = C, so its slope is equal to –A/B, or –2/–3, which equals 2/3. Therefore, the slope of line *m* must also be 2/3.

We are told that line *m* passes through the points (1, 4) and (2, a). The slope between these two points must equal 2/3. We can use the formula for the slope between two points and then set this equal to 2/3.

slope = (a – 4)/(2 – 1) = a – 4 = 2/3

a – 4 = 2/3

Multiply both sides by 3:

3(a – 4) = 2

3a – 12 = 2

Add 12 to both sides:

3a = 14

a = 14/3

### 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:**

3

-15

1/3

30

**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:**

6/5

12

5/6

12/5

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 #11 : 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 #1 : How To Find The Slope Of Parallel Lines

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 #11 : 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 #1 : How To Find The Slope Of Parallel Lines

Solve each problem and decide which is the best of the choices given.

What is the slope of a line parallel to the following equation of a line?

**Possible Answers:**

**Correct answer:**

Parallel lines have the same slope. So to find the slope of the given equation by getting the equation in slope-intercept form where is the slope of the line.

First, subtract both sides by giving you,

.

A parallel line would have a slope of .

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

Which of the following lines is parallel to ?

**Possible Answers:**

None of the given answers

**Correct answer:**

Remember that in order for two lines to be parallel, their slopes must be the same.

In slope-intercept form, a line's slope is the coefficient of .

For our given line, the slope, therefore, is . The only answer choice whose slope is also is .

Therefore, is the correct answer.

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