# Graphing Linear Equations Unit Test

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Philip Benanti
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Quizzes Created: 18 | Total Attempts: 27,224
Questions: 18 | Attempts: 975

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• 1.

• 2.

### What is the y intercept of the line?

• A.

0

• B.

1

• C.

2

• D.

4

B. 1
Explanation
The y-intercept of a line is the point where the line crosses the y-axis. In this case, the y-intercept is 1. This means that when x is equal to 0, the corresponding y value is 1.

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• 3.

### What is the slope of the line?

• A.

Positive

• B.

Negative

• C.

Zero

• D.

Undefined

A. Positive
Explanation
The slope of a line is a measure of how steep the line is. A positive slope means that the line is increasing as it moves from left to right. In other words, as the x-values increase, the y-values also increase. This can be visualized as a line that is slanting upwards from left to right on a graph.

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• 4.

### What is the slope of the line that passes through the points (-3,7) and (-9,4)?

• A.

1/2

• B.

10/13

• C.

-1/4

• D.

2

A. 1/2
Explanation
The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (-3,7) and (-9,4). Plugging these values into the formula, we get (4 - 7) / (-9 - (-3)) = -3 / -6 = 1/2. Therefore, the slope of the line is 1/2.

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• 5.

### Which line has a slope of 0?

• A.

Line A

• B.

Line B

• C.

Line C

• D.

Line D

B. Line B
Explanation
Line B has a slope of 0 because a line with a slope of 0 is a horizontal line. In other words, the line does not rise or fall as it extends horizontally. The slope of a line is determined by the change in the y-coordinates divided by the change in the x-coordinates between any two points on the line. Since a horizontal line has the same y-coordinate for all points, the change in y is always 0, resulting in a slope of 0.

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• 6.

### Which line has an undefined slope?

• A.

Line A

• B.

Line B

• C.

Line C

• D.

Line D

D. Line D
Explanation
Line D has an undefined slope because it is a vertical line. A vertical line has no change in the x-coordinate, resulting in a denominator of zero when calculating the slope using the formula (change in y / change in x). Since division by zero is undefined, the slope of a vertical line is undefined.

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• 7.

### The line y = -7 is:

• A.

Horizontal

• B.

Vertical

• C.

Neither

• D.

Cannot be determined

A. Horizontal
Explanation
The line y = -7 is horizontal because it has a fixed y-coordinate of -7, regardless of the value of x. In other words, all the points on this line have the same y-coordinate, while their x-coordinates can vary. This indicates that the line is parallel to the x-axis and does not have any vertical movement. Therefore, it can be concluded that the line y = -7 is horizontal.

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• 8.

### The line x = 5 is:

• A.

Horizontal

• B.

Vertical

• C.

Neither

• D.

Cannot be determined

B. Vertical
Explanation
The line x = 5 is vertical because it is a vertical line passing through the x-coordinate 5. Vertical lines have a constant x-coordinate and can intersect any y-coordinate, but they do not have a slope. In this case, the line x = 5 is a vertical line that intersects the y-axis at multiple points, making it a vertical line.

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• 9.

• A.

A

• B.

B

• C.

C

• D.

D

B. B
• 10.

### Which of the following lines is not perpendicular to

• A.

Y = 0.4 x – 7

• B.

-2x + 5y = 8

• C.

Y=(2/5)x + 4

• D.

2y = 5x + 1.5

D. 2y = 5x + 1.5
Explanation
The equation 2y = 5x + 1.5 is not perpendicular to y = 0.4x - 7 because the slopes of the two lines are not negative reciprocals of each other. The given equation has a slope of 5/2, while the equation y = 0.4x - 7 has a slope of 0.4. For two lines to be perpendicular, their slopes must be negative reciprocals of each other, meaning that when multiplied together, they equal -1. Since 0.4 * (5/2) does not equal -1, the line 2y = 5x + 1.5 is not perpendicular to y = 0.4x - 7.

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• 11.

### Which equation represents a line that intersects  at exactly one point?

• A.

Y = -(1/3)x - 5

• B.

Y = -(2/6)x + 10

• C.

Y = -(1/3)x + 3

• D.

Y = (1/3)x - 3

D. Y = (1/3)x - 3
Explanation
The equation y = (1/3)x - 3 represents a line that intersects the y-axis at -3 and has a slope of 1/3. Since the slope is not zero or undefined, the line will intersect the x-axis at exactly one point. Therefore, this equation represents a line that intersects at exactly one point.

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• 12.

### Which description best compares the graphs given by the equations 3x – y = 5 and 2x + 6y = 24?

• A.

Parallel

• B.

Coinciding

• C.

Perpendicular

• D.

Intersecting but not perpendicular

C. Perpendicular
Explanation
The given equations are 3x - y = 5 and 2x + 6y = 24. To determine the relationship between their graphs, we can rearrange both equations to slope-intercept form (y = mx + b). The first equation becomes y = 3x - 5, and the second equation becomes y = -1/3x + 4. The slopes of the two lines are 3 and -1/3, which are negative reciprocals of each other. When two lines have slopes that are negative reciprocals, they are perpendicular to each other. Therefore, the graphs of these equations are perpendicular.

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• 13.

### Which description best compares the graphs given by the equations x – 5y = -5 and 5x – 25y = 75?

• A.

Parallel

• B.

Coinciding

• C.

Perpendicular

• D.

Intersecting but not perpendicular

A. Parallel
Explanation
The given equations are in the form of linear equations. The equation x - 5y = -5 can be rewritten as y = (1/5)x + 1, while the equation 5x - 25y = 75 can be rewritten as y = (1/5)x - 3. Both equations have the same slope of 1/5, indicating that the graphs of the equations are parallel.

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• 14.

### Which equation represents a line parallel to the x-axis?

• A.

Y = -5

• B.

Y = -5x

• C.

X = 3

• D.

X = 3y

A. Y = -5
Explanation
The equation y = -5 represents a line parallel to the x-axis because the y-coordinate remains constant (-5) for all values of x. In other words, no matter what the value of x is, the y-coordinate will always be -5. This indicates that the line is horizontal and does not have any vertical change. Thus, it is parallel to the x-axis.

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• 15.

### What is an equation of the line that passes through the point (3,−1) and has a slope of 2?

• A.

Y = 2x + 5

• B.

Y = 2x − 1

• C.

Y = 2x – 4

• D.

Y = 2x - 7

A. Y = 2x + 5
Explanation
The equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is given as 2. The point (3, -1) lies on the line, so we can substitute these values into the equation. Plugging in x = 3 and y = -1, we get -1 = 2(3) + b. Solving for b, we find b = -7. Therefore, the equation of the line that passes through the point (3, -1) and has a slope of 2 is y = 2x + 5.

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• 16.

N/A
• 17.

### Write the equation of the line that is parallel to y = -x + 4 and goes through the point (6,-3).

N/A
Explanation
The equation of a line that is parallel to y = -x + 4 will have the same slope, which is -1. Using the point-slope form of a linear equation, we can plug in the coordinates of the given point (6,-3) and the slope (-1) to find the equation of the line. The equation will be y - (-3) = -1(x - 6), which simplifies to y + 3 = -x + 6.

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• 18.

### You start a lawn mowing service. You pay \$75 for the lawn mower and plan on charging \$25 per lawn. Write an equation to relate your income y to the number of lawns you mow x.

N/A
Explanation
The equation to relate your income y to the number of lawns you mow x is y = 25x - 75. This equation represents the total income (y) you earn by mowing x number of lawns. The \$75 is subtracted from the total income as it represents the initial cost of the lawn mower. The \$25 per lawn is then multiplied by the number of lawns mowed to calculate the income from mowing lawns.

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• Current Version
• Aug 25, 2023
Quiz Edited by
ProProfs Editorial Team
• Nov 17, 2014
Quiz Created by
Philip Benanti

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