Master Linear Functions: Graphing, Slope, and Equations

Question 1

Which graph illustrates a linear function with a positive slope?

Accepted Answer

A straight line rising from left to right

Answer

A straight line falling from left to right

Answer

A curved line that opens upward

Answer

A curved line that opens downward

Question 2

What is the y-intercept of the linear equation y = -x + 5?

Accepted Answer

5

Answer

0

Answer

1

Answer

10

Question 3

Which of the following sentences describes a key characteristic of linear functions?

Accepted Answer

A linear function has a constant slope.

Answer

A linear function always has a y-intercept of zero.

Answer

A linear function always passes through the origin.

Answer

All linear functions are curved.

Question 4

A store has a delivery charge of $10 and charges $3 for each item purchased. Which equation represents the total cost of an order?

Accepted Answer

y = 10 + 3x

Answer

y = 3x + 10

Answer

y = 10x + 3

Answer

y = 13x + 10

Question 5

What is the domain of a linear function?

Accepted Answer

All real numbers

Answer

Only positive numbers

Answer

Only negative numbers

Answer

Only integers

Question 6

Which of the following graphs represents a line with slope 2 and y-intercept -1?

Accepted Answer

[Image of a line with slope 2 and y-intercept -1]

Answer

[Image of a line with slope -2 and y-intercept 1]

Answer

[Image of a parabola]

Answer

[Image of a circle]

Question 7

What is the y-intercept of the line that passes through the point (0, -2) and has a slope of 3?

Accepted Answer

-6

Answer

-2

Answer

2

Answer

6

Question 8

What is the slope of a line that is horizontal?

Accepted Answer

0

Answer

1

Answer

-1

Answer

Undefined

Question 9

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

Accepted Answer

All real numbers

Answer

Integers only

Answer

Positive numbers only

Answer

Negative numbers only

Question 10

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

Accepted Answer

Exponential growth

Answer

Constant rate of change

Answer

Graph that is a straight line

Answer

y-value depends on the x-value

Question 11

Determine the slope of the line with the equation y = -3x + 2.

Accepted Answer

-3

Answer

2

Answer

3

Answer

-2

Question 12

Find the y-intercept of the line y = 2x + 3.

Accepted Answer

3

Answer

2

Answer

-2

Answer

-3

Question 13

Which of the following equations represents a horizontal line?

Accepted Answer

y = 2

Answer

y = x + 2

Answer

y = 2x

Answer

y = -x + 2

Question 14

A car travels 120 miles in 2 hours. What is the average speed of the car in miles per hour?

Accepted Answer

60

Answer

30

Answer

90

Answer

120

Question 15

Find the equation of a line that is parallel to the x-axis and passes through the point (3, 2).

Accepted Answer

y = 2

Answer

y = 3

Answer

y = x + 2

Answer

y = 2x + 3

Question 16

Which of the following graphs represents a line with a positive slope?

Accepted Answer

A line sloping upwards from left to right

Answer

A line sloping downwards from left to right

Answer

A horizontal line

Answer

A vertical line

Question 17

Which of the following is the equation of a line that is parallel to the line 2x - y = 3?

Accepted Answer

2x + y = 3

Answer

2x - y = -3

Answer

x + 2y = 3

Answer

x - 2y = 3

Question 18

The graph of a linear function has a y-intercept of -2. What is the equation of the function?

Accepted Answer

y = -2

Answer

y = -2x

Answer

y = 2x - 2

Answer

y = -2x + 2

Question 19

Which of the following graphs best represents a linear function?

Accepted Answer

A straight line

Answer

A circle

Answer

A parabola

Answer

A hyperbola

Question 20

What happens to the graph of a linear function when its slope changes?

Accepted Answer

The graph becomes steeper or less steep.

Answer

The graph moves up or down.

Answer

The graph changes from a line to a curve.

Question 21

In the United States, what is the slope of the line represented by the equation y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

-5

Answer

5

Question 22

In the United States, what is the equation of the line with a slope of 2 and passing through the point (1, 3)?

Accepted Answer

y = 2x + 1

Answer

y = 2x - 1

Answer

y = x + 2

Answer

y = x - 2

Question 23

In the United States, which of the following graphs represents the line y = -x + 2?

Accepted Answer

A graph of a line with a downward slope.

Answer

A graph of a line with an upward slope.

Answer

A graph of a horizontal line.

Answer

A graph of a vertical line.

Question 24

In the United States, what is the slope of the line that is perpendicular to the line y = 2x - 3?

Accepted Answer

-1/2

Answer

2

Answer

-2

Answer

1/2

Question 25

In the United States, which of the following is the equation of the line that is parallel to the line y = -3x + 4 and has a y-intercept of 2?

Accepted Answer

y = -3x + 2

Answer

y = -3x - 2

Answer

y = x + 2

Answer

y = x - 2

Question 26

In the United States, what is the domain of the linear function y = 2x + 1?

Accepted Answer

All real numbers

Answer

Only positive numbers

Answer

Only negative numbers

Answer

Only integers

Question 27

In the United States, which of the following is the range of the linear function y = -x + 3?

Accepted Answer

All real numbers

Answer

Only positive numbers

Answer

Only negative numbers

Answer

Only integers

Question 28

Which equation represents a vertical line passing through the point (2, -3)?

Accepted Answer

x = 2

Answer

y = 2

Answer

y = -3

Answer

x = -3

Question 29

Which of these equations represents a line with slope = 2 and y-intercept = -3?

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 3

Question 30

What is the slope of a horizontal line?

Accepted Answer

0

Answer

1

Answer

-1

Answer

Undefined

Question 31

Which of the following is the graph of the line **y = -x + 2**?

Accepted Answer

A line with a negative slope

Answer

A line with a positive slope

Answer

A vertical line

Answer

A horizontal line

Question 32

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

Accepted Answer

-1/2

Answer

1/2

Answer

2

Answer

-2

Question 33

Which of the following equations represents a line that has the same slope as the line **y = -3x + 4** but a different y-intercept?

Accepted Answer

y = -3x + 5

Answer

y = -3x - 4

Answer

y = 3x + 4

Answer

y = 3x - 5

Question 34

What is the area of the triangle formed by the points (0, 0), (3, 4), and (4, 0)?

Accepted Answer

6

Answer

8

Answer

10

Answer

12

Question 35

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

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 36

Which of the following graphs represents the line with equation y = 2?

Accepted Answer

A horizontal line passing through the point (0, 2)

Answer

A vertical line passing through the point (2, 0)

Answer

A line with a positive slope passing through the origin

Answer

A line with a negative slope passing through the origin

Question 37

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

Accepted Answer

-5

Answer

3

Answer

-3

Answer

5

Question 38

Which of the following statements about parallel lines is true?

Accepted Answer

Parallel lines have the same slope.

Answer

Parallel lines have different slopes.

Answer

Parallel lines intersect at a right angle.

Answer

Parallel lines never intersect.

Question 39

A store is selling apples for $0.50 each. Which of the following equations represents the total cost of buying 'x' apples?

Accepted Answer

y = 0.5x

Answer

y = x ÷ 0.5

Answer

y = 0.5x + 1

Answer

y = x - 0.5

Question 40

Which of the following graphs represents a linear function?

Accepted Answer

A straight line passing through the origin

Answer

A parabola opening upwards

Answer

A circle centered at the origin

Answer

A hyperbola with its center at the origin

Question 41

Which of the following equations represents a line with a slope of -2 and a y-intercept of 1?

Accepted Answer

y = -2x + 1

Answer

y = 2x + 1

Answer

y = -2x - 1

Answer

y = 2x - 1

Question 42

Which of the following inequalities represents the graph of a line that is below the x-axis?

Accepted Answer

y < 0

Answer

y > 0

Answer

y ≤ 0

Answer

y ≥ 0

Question 43

Which of the following equations represents a line with a slope of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

y = -2x + 3

Answer

y = -3x + 2

Question 44

What is the equation of the line that passes through the point (1, 4) and has a slope of -1?

Accepted Answer

y = -x + 3

Answer

y = -x + 5

Answer

y = x - 3

Answer

y = x - 5

Question 45

What is the slope of the line that is parallel to the x-axis?

Accepted Answer

0

Answer

1

Answer

-1

Answer

Undefined

Question 46

Which of the following is the x-coordinate of the point where the lines y = x + 2 and y = 2x - 3 intersect?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 47

Which of the following inequalities represents the shaded region below the line y = x + 1?

Accepted Answer

y < x + 1

Answer

y > x + 1

Answer

y = x + 1

Answer

y > -x + 1

Question 48

The equation of a line has a slope of 3 and a y-intercept of 2. What is the equation of the line?

Accepted Answer

y = 3x + 2

Answer

y = 2x + 3

Answer

y = 2x - 3

Answer

y = 3x - 2

Question 49

Which of the following best describes the graph of a linear function?

Accepted Answer

A straight line

Answer

A curved line

Answer

A circle

Answer

A triangle

Question 50

A linear function has a y-intercept of 5 and a slope of 3. What is the equation of the function?

Accepted Answer

y = 3x + 5

Answer

y = 5x + 3

Answer

y = -3x + 5

Answer

y = -5x + 3

Question 51

Which of the following graphs represents a linear function with a negative slope?

Accepted Answer

A line sloping downwards from left to right

Answer

A line sloping upwards from left to right

Answer

A horizontal line

Answer

A vertical line

Question 52

Find the slope of the line that is parallel to the y-axis.

Accepted Answer

Undefined

Answer

0

Answer

1

Answer

-1

Question 53

Consider the scenario of a job where total pay depends linearly on hours worked. Which of these represents the slope of the corresponding line?

Accepted Answer

Hourly wage

Answer

Total pay earned

Answer

Hours worked

Answer

Overtime pay

Question 54

Identify which equation represents a linear function:

Accepted Answer

y = 2x + 5

Answer

y = 3x^2 + 2x - 1

Answer

y = x^3 - 4x + 2

Answer

y = 1/(x + 1)

Question 55

Given the line defined by the equation y = -2x + 6, determine its y-intercept.

Accepted Answer

6

Answer

-2

Answer

2

Answer

-6

Question 56

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

Accepted Answer

A line with a negative slope

Answer

A line with a positive slope

Answer

A parabola

Answer

A circle

Question 57

Write the equation for the line passing through the point (1, 2) and having a slope of 3.

Accepted Answer

y = 3x + 2

Answer

y = 3x - 1

Answer

y = 2x + 3

Answer

y = 2x - 1

Question 58

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

Accepted Answer

y = -1/2x + 7/2

Answer

y = 1/2x + 5/2

Answer

y = 2x + 2

Answer

y = -2x + 10

Question 59

Solve the system of linear equations: y = 2x - 5 and y = x + 1.

Accepted Answer

(3, -2)

Answer

(2, -3)

Answer

(4, -1)

Answer

(5, 0)

Question 60

Which of the following is the equation of a line passing through the point (2, 5) with a slope of 3?

Accepted Answer

y = 3x + 1

Answer

y = x + 1

Answer

y = x + 3

Answer

y = 3x - 1

Question 61

A line has a slope of -3 and a y-intercept of 2. What is its equation?

Accepted Answer

y = -3x + 2

Answer

y = 3x - 2

Answer

y = -2x + 3

Answer

y = 2x - 3

Question 62

Which of the following is the equation of the line perpendicular to y = 2x + 1 and passing through the point (2, 3)?

Accepted Answer

y = -1/2x + 4

Answer

y = 1/2x + 4

Answer

y = -2x + 7

Answer

y = 2x + 7

Question 63

Which of the following is the equation of 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 64

Which of the options below accurately represents a linear function: a straight line, a parabola, a circle, or a hyperbola?

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

A hyperbola