Linear Functions: Master the Basics with Interactive Quizzes

Question 1

Identify the equation that represents a linear function:

Accepted Answer

y = mx + b

Answer

y = mx^2 + b

Answer

y = x^3 + b

Answer

y = 1/x + b

Question 2

Determine the slope of the linear function represented by the equation y = 3x - 2:

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 3

Which graph represents the linear function y = -2x + 3?

Accepted Answer

[Image of a line with slope -2 and y-intercept 3]

Answer

[Image of a line with slope 2 and y-intercept 3]

Answer

[Image of a parabola opening up]

Answer

[Image of a parabola opening down]

Question 4

Find the x-intercept of the linear function y = 2x - 4:

Accepted Answer

2

Answer

0

Answer

-2

Answer

4

Question 5

Determine the y-intercept of the linear function y = -3x + 5:

Accepted Answer

5

Answer

0

Answer

3

Answer

-5

Question 6

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

Accepted Answer

All real numbers

Answer

Positive numbers only

Answer

Negative numbers only

Answer

Integers only

Question 7

Determine the range of the linear function y = -2x + 3:

Accepted Answer

All real numbers

Answer

Positive numbers only

Answer

Negative numbers only

Answer

Integers only

Question 8

Identify the linear function that is parallel to the line y = 2x - 1:

Accepted Answer

y = 2x + 3

Answer

y = -2x - 1

Answer

y = -2x + 3

Answer

y = 1/2x - 1

Question 9

Which linear function is perpendicular to the line y = -x + 2?

Accepted Answer

y = x + 2

Answer

y = -x - 2

Answer

y = 2x + 2

Answer

y = -2x + 2

Question 10

Determine the equation of the line that passes through the given points: (2, 5) and (-1, 1).

Accepted Answer

y = -2x + 5

Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = -x + 7

Question 11

Find the slope of the line given by the equation: y = -3x + 2.

Accepted Answer

-3

Answer

3

Answer

-2

Answer

2

Question 12

Which characteristic is unique to linear functions?

Accepted Answer

Constant slope

Answer

Vertical intercepts

Answer

Quadratic graphs

Answer

Asymptotic behavior

Question 13

Solve for x: 2x + 5 = 13

Accepted Answer

4

Answer

5

Answer

6

Answer

7

Question 14

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

Accepted Answer

y = 2x + 5

Answer

y = -2x + 7

Answer

y = 2x - 1

Answer

y = -2x + 3

Question 15

Determine the domain and range of the function: f(x) = 2x - 5.

Accepted Answer

Domain: all real numbers, Range: all real numbers

Answer

Domain: all real numbers, Range: y < 5

Answer

Domain: x != 5, Range: all real numbers

Answer

Domain: x > 5, Range: y > 5

Question 16

Find the inverse of the function: f(x) = 3x + 2.

Accepted Answer

f^-1(x) = (x - 2)/3

Answer

f^-1(x) = 3x - 2

Answer

f^-1(x) = 2x + 3

Answer

f^-1(x) does not exist

Question 17

Find the x-intercept of the line y = 3x - 6.

Accepted Answer

2

Answer

-2

Answer

3

Answer

-3

Question 18

What is the y-intercept of the line represented by the equation 2x - 3y = 6?

Accepted Answer

-2

Answer

-3

Answer

3

Answer

2

Question 19

What is the slope of a line that is parallel to the line represented by the equation y = -2x + 1?

Accepted Answer

-2

Answer

2

Answer

1

Answer

-1

Question 20

What is the domain of the linear function f(x) = 2x - 3?

Accepted Answer

All real numbers

Answer

Positive real numbers

Answer

Negative real numbers

Answer

Integers

Question 21

What is the range of the linear function f(x) = -x + 2?

Accepted Answer

All real numbers

Answer

Integers

Answer

Positive real numbers

Answer

Negative real numbers

Question 22

What is the slope of the line represented by the equation y = -2x + 5?

Accepted Answer

-2

Answer

5

Answer

2

Answer

-5

Question 23

Which equation represents a line with a slope of 3 and a y-intercept of -1?

Accepted Answer

y = 3x - 1

Answer

y = -3x + 1

Answer

y = 3x + 1

Answer

y = -3x - 1

Question 24

A car rental company charges a flat fee of $25 plus $0.50 per mile driven.  Which equation represents the total cost (C) of renting a car for 'm' miles?

Accepted Answer

C = 0.50m + 25

Answer

C = 25m + 0.50

Answer

C = 0.50m

Answer

C = 25m

Question 25

What is the y-intercept of the line that passes through the points (2, 5) and (4, 9)?

Accepted Answer

(0, 1)

Answer

(1, 0)

Answer

(0, -1)

Answer

(-1, 0)

Question 26

Which of the following describes the relationship between the lines represented by the equations y = 2x + 3 and y = 2x - 1?

Accepted Answer

Parallel

Answer

Intersecting but not perpendicular

Answer

Coincident

Answer

Perpendicular

Question 27

The cost of producing 'x' items is given by the function C(x) = 500 + 10x. What does the slope of this function represent?

Accepted Answer

The cost of producing one additional item

Answer

The total cost of producing 10 items

Answer

The number of items produced

Answer

The fixed cost of production

Question 28

What is the slope of the line represented by the equation y = 2x + 3?

Accepted Answer

2

Answer

3

Answer

-3

Answer

-2

Question 29

Which of the following points lies on the line represented by the equation y = -x + 4?

Accepted Answer

(2, 2)

Answer

(0, 0)

Answer

(1, 5)

Answer

(3, 1)

Question 30

A car travels at a constant speed of 60 miles per hour. Which equation represents the distance (d) the car travels in terms of time (t) in hours?

Accepted Answer

d = 60t

Answer

d = 60/t

Answer

d = t + 60

Answer

t = 60d

Question 31

What is the y-intercept of the line represented by the equation 3x + 2y = 6?

Accepted Answer

(0, 3)

Answer

(3, 0)

Answer

(2, 0)

Answer

(0, 2)

Question 32

The graph of a linear function passes through the points (1, 2) and (3, 6). What is the slope of this line?

Accepted Answer

2

Answer

1

Answer

-1

Answer

-2

Question 33

Which of the following equations represents a line that is parallel to the line y = 4x - 1?

Accepted Answer

y = 4x + 5

Answer

y = -x + 1

Answer

y = (1/4)x - 1

Answer

y = -4x - 1

Question 34

A line has a slope of -3 and passes through the point (2, 5). What is the equation of this line in slope-intercept form?

Accepted Answer

y = -3x + 11

Answer

y = 3x + 11

Answer

y = -3x - 1

Answer

y = 3x - 1

Question 35

The cost of a taxi ride is $2.50 plus $1.50 per mile. Which equation represents the cost (C) of a taxi ride in terms of the number of miles (m) traveled?

Accepted Answer

C = 1.5m + 2.5

Answer

C = 4m

Answer

C = 2.5m + 1.5

Answer

C = m + 4

Question 36

What is the equation of the line that passes through the points (0, 4) and (2, 0)?

Accepted Answer

y = -2x + 4

Answer

y = -x + 4

Answer

y = 2x + 4

Answer

y = x + 4

Question 37

Which of the following is NOT a characteristic of a linear function?

Accepted Answer

The graph is a curve.

Answer

The equation can be written in slope-intercept form.

Answer

The rate of change is constant.

Answer

The graph is a straight line.

Question 38

Identify the linear function that has a slope of -3 and passes through the point (2, 5).

Accepted Answer

y = -3x + 11

Answer

y = 3x - 11

Answer

y = 3x + 1

Answer

y = -3x - 1

Question 39

Which of the following equations represents a vertical line passing through the x-axis at x = 5?

Accepted Answer

x = 5

Answer

y = 0

Answer

y = 5

Answer

x = 0

Question 40

Determine the slope of the line passing through the points (-2, 1) and (4, 7).

Accepted Answer

1.5

Answer

0.5

Answer

2

Question 41

Find the y-intercept of the linear function 2x - 3y = 6

Accepted Answer

2

Answer

-2

Answer

-3

Answer

3

Question 42

Graph the linear function y = 2x + 1:

Accepted Answer

/path/to/image.png

Answer

/path/to/incorrect_image1.png

Answer

/path/to/incorrect_image2.png

Answer

/path/to/incorrect_image3.png

Question 43

Write the equation of the linear function that has a slope of 0 and passes through the point (3, -5).

Accepted Answer

y = -5

Answer

y = 5

Answer

y = 0

Answer

y = 3

Question 44

Determine the domain and range of the linear function f(x) = -2x + 4.

Accepted Answer

Domain: all real numbers; Range: all real numbers

Answer

Domain: all real numbers; Range: all positive numbers

Answer

Domain: all negative numbers; Range: all negative numbers

Answer

Domain: all positive integers; Range: all positive integers

Question 45

Solve for x in the linear equation: 5x - 10 = 25

Accepted Answer

7

Answer

9

Answer

11

Answer

5

Question 46

Apply the linear function f(x) = 3x - 5 to the value x = 2:

Accepted Answer

1

Answer

5

Answer

-1

Answer

7

Question 47

What is the slope of the line passing through the points (2, 5) and (4, 9)?

Accepted Answer

2

Answer

-1/2

Answer

-2

Answer

1/2

Question 48

Which of the following equations represents a linear function?

Accepted Answer

y = 3x - 2

Answer

y = |x| + 4

Answer

y = 2/x

Answer

y = x^2 + 1

Question 49

A car rental company charges a flat fee of $25 plus $0.30 per mile driven. Which equation represents the total cost (C) of renting a car for 'm' miles?

Accepted Answer

C = 0.30m + 25

Answer

C = 25m + 0.30

Answer

C = 0.30m

Answer

C = 25m

Question 50

What is the y-intercept of the line represented by the equation y = -2x + 7?

Accepted Answer

7

Answer

-2

Answer

-7

Answer

2

Question 51

Which of the following lines is parallel to the line y = 4x - 1?

Accepted Answer

y = 4x + 5

Answer

y = - (1/4)x + 1

Answer

y = -4x + 2

Answer

y = (1/4)x - 3

Question 52

The graph of a linear function is shown below. What is the x-intercept of the function? (Assume each grid unit represents one unit)

Accepted Answer

(-2, 0)

Answer

(0, 4)

Answer

(0, -4)

Answer

(2, 0)

Question 53

Which of the following situations can be modeled by a linear function?

Accepted Answer

The height of a candle burning at a constant rate over time.

Answer

The area of a circle as the radius increases.

Answer

The population of bacteria doubling every hour.

Question 54

If f(x) = 2x - 5, what is the value of f(3)?

Accepted Answer

1

Answer

-1

Answer

11

Answer

-11

Question 55

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

Accepted Answer

y = -2x + 5

Answer

y = -2x - 1

Answer

y = 2x + 1

Answer

y = 2x + 5

Question 56

The cost of producing 'x' units of a product is given by C(x) = 500 + 10x. What does the number '10' represent in the context of this scenario?

Accepted Answer

The cost of producing each additional unit.

Answer

The revenue generated from selling 'x' units.

Answer

The total cost of producing 'x' units.

Answer

The fixed cost of production.