Graphing Linear Functions: Master the Art of Plotting Lines

Question 1

Which of these is NOT a characteristic of a linear function?

Accepted Answer

Has a range of all real numbers

Answer

Has a constant rate of change

Answer

Graphs as a straight line

Answer

Has a domain of all real numbers

Question 2

What is the domain of the linear function y = 2x - 5?

Accepted Answer

All real numbers

Answer

All positive numbers

Answer

All negative numbers

Answer

Only 0

Question 3

Which equation represents a vertical line?

Accepted Answer

x = 3

Answer

y = 2

Answer

y = 4x - 5

Answer

x = -2y + 7

Question 4

What is the x-intercept of the line represented by the equation 2x - 5y = 10?

Accepted Answer

2.5

Answer

5

Answer

10

Answer

20

Question 5

Identify the domain of the function f(x) = (x - 3)/(x + 2).

Accepted Answer

All real numbers except -2

Answer

All real numbers

Answer

All real numbers except 3

Answer

All real numbers greater than 2

Question 6

Find the range of the function f(x) = |x - 2|.

Accepted Answer

All non-negative real numbers

Answer

All real numbers

Answer

All negative real numbers

Answer

Only the number 2

Question 7

Which of the following transformations will result in a graph that is a vertical shift up by 2 units of the graph of y = x?

Accepted Answer

f(x) = x + 2

Answer

f(x) = 2x

Answer

f(x) = x^2

Answer

f(x) = 1/x

Question 8

Which equation represents a line with a slope of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = -2x - 3

Answer

y = -2x + 3

Question 9

Identify the domain of the function f(x) = 3x - 2.

Accepted Answer

All real numbers

Answer

Positive real numbers

Answer

Negative real numbers

Answer

Integers

Question 10

Find the equation of the line that is perpendicular to y = x + 2 and passes through the point (-2, 1).

Accepted Answer

y = -x + 1

Answer

y = -x

Answer

y = x

Answer

y = x + 1

Question 11

Determine the range of the function f(x) = -3x + 5.

Accepted Answer

All real numbers

Answer

Positive real numbers

Answer

Negative real numbers

Answer

Integers

Question 12

What is the slope-intercept form of a linear equation?

Accepted Answer

y = mx + c

Answer

y - y₁ = m(x - x₁)

Answer

mx + c = y

Answer

(y - c)/m = x

Question 13

Find the equation of a line parallel to y = 2x - 1 passing through the point (3, 5):

Accepted Answer

y = 2x + 5

Answer

y = 2x - 5

Answer

y = -2x + 5

Answer

y = -2x - 5

Question 14

How does the slope of a linear function impact the steepness of its graph?

Accepted Answer

A greater slope leads to a steeper graph.

Answer

A greater slope leads to a flatter graph.

Answer

The slope has no effect on the graph's steepness.

Answer

A smaller slope leads to a steeper graph.

Question 15

Which of the following equations represents a line that passes through the point (2, 5) and has a slope of 3?

Accepted Answer

y = 3x + 1

Answer

y = 3x - 1

Answer

y = x + 5

Answer

y = x - 5

Question 16

Which equation represents a line with a slope of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = -2x + 3

Answer

y = 3x - 2

Question 17

Which equation below represents a horizontal line passing through the y-axis?

Accepted Answer

y = 3

Answer

y = 2x + 3

Answer

x = -2

Answer

y = mx + b

Question 18

What is the equation of the line with a slope of 3 and a y-intercept of -2?

Accepted Answer

y = 3x - 2

Answer

y = -2x + 3

Answer

y = 2x - 3

Answer

y = -3x + 2

Question 19

Which of the following statements is true about the line y = -2x + 1?

Accepted Answer

It intersects the y-axis at (0, 1).

Answer

It has a positive slope.

Answer

It is parallel to the x-axis.

Answer

It is perpendicular to the y-axis.

Question 20

Find the equation of the line through the point (3, -4) and parallel to the line y = 2x - 1.

Accepted Answer

y = 2x - 10

Answer

y = 2x + 2

Answer

y = -2x - 10

Answer

y = -2x + 2

Question 21

Which inequality represents the solution region of the graph y < x + 2?

Accepted Answer

y < x + 2

Answer

y > x + 2

Answer

y = x + 2

Answer

y ≤ x + 2

Question 22

Find the domain of the function f(x) = √(x - 3).

Accepted Answer

x > 3

Answer

x ≥ 3

Answer

x < 3

Answer

(-3, ∞)

Question 23

Which equation represents a vertical line that passes through the point (2, 5)?

Accepted Answer

x = 2

Answer

y = 5

Answer

y = 2x + 5

Answer

x - 2 = 0

Question 24

Which of the following is the slope-intercept form of a linear function?

Accepted Answer

y = mx + b

Answer

y = mx

Answer

x = my + b

Answer

y - y1 = m(x - x1)

Question 25

Calculate the slope of the line passing through the points (2, 3) and (6, 9).

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 26

Write the equation of a line with a slope of -1/2 and a y-intercept of 3.

Accepted Answer

y = -1/2x + 3

Answer

y = ½x + 3

Answer

y = -1/2x - 3

Answer

y = ½x - 3

Question 27

Determine the domain of the function y = -2x + 5.

Accepted Answer

All real numbers

Answer

All positive numbers

Answer

All negative numbers

Answer

Only zero

Question 28

Write an inequality that represents the shaded region below the line y = x + 2.

Accepted Answer

y < x + 2

Answer

y > x + 2

Answer

y x + 2

Answer

y x + 2

Question 29

Which transformation will shift the graph of the line y = 2x + 1 up by 3 units?

Accepted Answer

y = 2x + 4

Answer

y = 2x - 2

Answer

y = 2(x + 3) + 1

Answer

y = 2(x - 3) + 1

Question 30

For the equation y = -2x + 5, what is the y-intercept?

Accepted Answer

5

Answer

-2

Answer

2

Answer

-5

Question 31

Determine the range of the function f(x) = |x - 3|.

Accepted Answer

y ≥ 0

Answer

All real numbers

Answer

y ≤ 0

Answer

y ≥ 3

Question 32

Which equation represents a horizontal line?

Accepted Answer

y = 2

Answer

x = 3

Answer

y = x + 1

Answer

y = 2x - 5

Question 33

Which of the following is the standard form of a linear equation?

Accepted Answer

Ax + By = C

Answer

y = mx + c

Answer

y = c

Answer

x = mx + c

Question 34

Find the slope of the line passing through the points (1, 3) and (3, 7).

Accepted Answer

2

Answer

1

Answer

4

Answer

8

Question 35

Which of the following is the equation of the line with a slope of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = -2x + 1

Answer

x = 2y - 1

Answer

x = -2y + 1

Question 36

Identify the type of slope for the linear function represented by the equation y = 0.

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Answer

Undefined

Question 37

Determine if the lines represented by the equations y = -x + 2 and 2x + y = 4 are parallel.

Accepted Answer

No

Answer

Yes

Question 38

Which of the following equations represents the slope-intercept form of a linear function?

Accepted Answer

y = mx + b

Answer

y - y1 = m(x - x1)

Answer

Ax + By = C

Answer

x/a + y/b = 1

Question 39

What is the slope of the linear function passing through the points (-2, 3) and (4, 9)?

Accepted Answer

3/2

Answer

1

Answer

2/3

Answer

-3/2

Question 40

What is the equation of the line parallel to y = -x + 2 and passing through the point (3, 5)?

Accepted Answer

y = -x + 5

Answer

y = -x - 1

Answer

y = x + 5

Answer

y = x - 1

Question 41

What is the slope of the line perpendicular to the line y = 2x + 1?

Accepted Answer

-1/2

Answer

1/2

Answer

2

Answer

-2

Question 42

Which of the following equations represents a horizontal linear function?

Accepted Answer

y = 3

Answer

y = 2x + 4

Answer

y = x - 1

Answer

y = -2x + 3

Question 43

Which of the following equations represents the slope-intercept form of a linear function?

Accepted Answer

y = mx + b

Answer

y = mx - b

Answer

y - y1 = m(x - x1)

Answer

x = my + b

Question 44

What is the slope of the linear function passing through the points (1, 3) and (3, 7)?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 45

What is the y-intercept of the line with the equation y = 3x - 5?

Accepted Answer

-5

Answer

2

Answer

5

Answer

10

Question 46

Which of the following equations represents the point-slope form of a linear function?

Accepted Answer

y - y1 = m(x - x1)

Answer

y = mx + b

Answer

x = my + b

Answer

x - x1 = m(y - y1)

Question 47

What is the domain of the linear function y = 5x - 2?

Accepted Answer

All real numbers

Answer

x ≥ 0

Answer

x > 0

Answer

x < 0

Question 48

What is the range of the linear function y = -4x + 4?

Accepted Answer

All real numbers

Answer

y ≥ 0

Answer

y > 0

Answer

y < 0