Master Linear Equations: A Comprehensive Guide for High School Seniors

Question 1

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

Accepted Answer

Parabolic graph

Answer

Constant rate of change

Answer

Straight line graph

Answer

Negative slope

Question 2

Find the y-intercept of the line represented by the equation: 2x + 5y = 10.

Accepted Answer

5

Answer

-2

Answer

10

Answer

-10

Question 3

Solve the linear equation with decimals: 0.5x + 2 = -1

Accepted Answer

x = -4

Answer

x = 4

Answer

x = -6

Answer

x = 6

Question 4

Find the domain of the linear equation: y = 1/(x - 2)

Accepted Answer

All real numbers except 2

Answer

All real numbers except 0

Answer

All real numbers

Answer

All positive real numbers

Question 5

Identify the equation of a line:

Accepted Answer

y = 2x + 1

Answer

y = x^2 - 1

Answer

y = sin(x)

Answer

y = 1 / x^2

Question 6

Graph the linear equation y = -2x + 3:

Accepted Answer

Negative slope

Answer

Positive slope

Answer

Parabola

Answer

Circle

Question 7

Calculate the slope of 3x + 2y = 6:

Accepted Answer

2/3

Answer

-3/2

Answer

-2/3

Answer

3/2

Question 8

Graph the linear equation y = 2/3x + 1:

Accepted Answer

Positive slope

Answer

Negative slope

Answer

Parabola

Answer

Circle

Question 9

Calculate the slope of the line that passes through the points (2, 5) and (4, 9).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 10

Find the solution set of the inequality: 2x + 5 > 15

Accepted Answer

x > 5

Answer

x < 5

Answer

x < -5

Answer

x > -5

Question 11

Identify the option that is NOT a solution to the system of equations: y = 2x + 1 and y = x - 1

Accepted Answer

(0, -1)

Answer

(1, 1)

Answer

(2, 3)

Answer

(3, 5)

Question 12

Solve the equation: 2x + 5 equals 13.

Accepted Answer

x equals 3

Answer

x equals 4

Answer

x equals 5

Answer

x equals 6

Question 13

Solve the equation: x/2 - 3 equals 5.

Accepted Answer

x equals 16

Answer

x equals 18

Answer

x equals 20

Answer

x equals 22

Question 14

Solve the equation: 2x + 0.5 equals 6.5

Accepted Answer

x equals 3.5

Answer

x equals 3

Answer

x equals 4

Answer

x equals 4.5

Question 15

Find the slope of the line: y equals -3x + 2

Accepted Answer

-3

Answer

3

Answer

2

Answer

-2

Question 16

Find the y-intercept of the line: y equals 2x + 5

Accepted Answer

5

Answer

2

Answer

7

Answer

10

Question 17

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7

Question 18

Solve the equation: 2/3x + 1 = 5

Accepted Answer

x = 9

Answer

x = 6

Answer

x = 12

Answer

x = 15

Question 19

Which of the following is NOT an equation of a line?

Accepted Answer

y = x^2

Answer

y = 2x + 1

Answer

x + y = 5

Answer

y = -3

Question 20

What is a defining characteristic of linear functions?

Accepted Answer

They have a constant rate of change.

Answer

Their graphs are curved lines.

Answer

They can have multiple y-intercepts.

Answer

Their equations are in the form ax^2 + bx + c = 0.

Question 21

Solve the linear equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7

Question 22

Find the slope of the line represented by this equation: y = 3x - 2

Accepted Answer

3

Answer

-3

Answer

1

Answer

-1

Question 23

Find the y-intercept of the line represented by this equation: y = -2x + 5

Accepted Answer

5

Answer

2

Answer

-2

Answer

-5

Question 24

Solve the system of equations: 2x + 3y = 11, x - y = 3

Accepted Answer

(x = 3, y = 2)

Answer

(x = 2, y = 1)

Answer

(x = 4, y = 3)

Answer

(x = 5, y = 4)

Question 25

Solve the linear equation: 3(y - 2) = 12

Accepted Answer

y = 8

Answer

y = 4

Answer

y = 6

Answer

y = 10

Question 26

Which graph represents the linear equation: y = 2x - 1?

Accepted Answer

A graph with a slope of 2 and a y-intercept of -1

Answer

A graph with a slope of 1 and a y-intercept of -2

Answer

A graph with a slope of 2 and a y-intercept of 1

Answer

A graph with a slope of 1 and a y-intercept of 2

Question 27

Find the y-intercept of the linear equation: 2x + 3y = 6

Accepted Answer

1

Answer

-2

Answer

-1

Answer

2

Question 28

Which of the following is a linear equation in one variable?

Accepted Answer

2x + 3y = 6

Answer

x^2 + y = 5

Answer

y = e^x

Answer

sin(x) = cos(y)

Question 29

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7

Question 30

Which of the following equations represents a line parallel to the x-axis?

Accepted Answer

y = 2

Answer

y = 2x

Answer

y = 2x + 1

Answer

y = 2x - 1

Question 31

Which of the following equations represents a line perpendicular to the y-axis?

Accepted Answer

x = 2

Answer

y = 2x

Answer

y = 2x + 1

Answer

y = 2x - 1

Question 32

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

Answer

y = 3x - 2

Question 33

What is the slope of the line that passes through the points (2, 5) and (4, 1)?

Accepted Answer

-2

Answer

2

Answer

1/2

Answer

-1/2

Question 34

What is the solution to the equation (2/3)x - (1/4) = (5/6)?

Accepted Answer

x = 2

Answer

x = 1

Answer

x = 3

Answer

x = 4

Question 35

Which equation represents the line shown in the graph below? (Insert a graph of a line with a negative slope and a y-intercept of 2)

Accepted Answer

y = -x + 2

Answer

y = x + 2

Answer

y = x - 2

Answer

y = -x - 2

Question 36

A taxi charges a flat fee of $3.00 plus $0.50 per mile.  Which equation represents the total cost (C) of a taxi ride in terms of the number of miles (m)?

Accepted Answer

C = 0.5m + 3

Answer

C = 3m + 0.5

Answer

C = 3.5m

Answer

C = m + 3

Question 37

What is the y-intercept of the line represented by the equation 4x - 2y = 8?

Accepted Answer

-4

Answer

4

Answer

2

Answer

-2

Question 38

What is the slope of the line represented by the equation y = -3x + 5?

Accepted Answer

-3

Answer

-5

Answer

5

Answer

3

Question 39

Which of the following points lies on the line represented by the equation y = 2x - 1?

Accepted Answer

(2, 3)

Answer

(0, 2)

Answer

(1, 1)

Answer

(3, 1)

Question 40

What is the solution to the equation 3x - 2 = 7x + 4?

Accepted Answer

x = -1.5

Answer

x = -1

Answer

x = 0

Answer

x = 1

Question 41

Which graph represents the linear equation  *y = 2x - 1*?

Accepted Answer

Select an image showing the graph of y = 2x - 1

Answer

Select an image showing the graph of y = -2x + 1

Answer

Select an image showing the graph of y = x + 1

Answer

Select an image showing the graph of y = 2x + 1

Question 42

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

Accepted Answer

3

Answer

4

Answer

2

Answer

1

Question 43

What is the y-intercept of the linear equation *2x + y = 5*?

Accepted Answer

(0, 5)

Answer

(0, 4)

Answer

(2, 0)

Answer

(3, 0)

Question 44

Which of the following equations is NOT a linear equation?

Accepted Answer

y = x^2 + 1

Answer

y = 2x + 3

Answer

y = 3 - x

Answer

y = 0.5x - 1

Question 45

Solve the following system of linear equations:

*x + y = 5*
*x - y = 1*

Accepted Answer

x = 3, y = 2

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Answer

x = 2, y = 3

Question 46

Solve for *x* in the equation: *3x + 5 = 14*

Accepted Answer

x = 3

Answer

x = 6

Answer

x = 1

Answer

x = -3

Question 47

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

Accepted Answer

2

Answer

3

Answer

-3

Answer

-2

Question 48

The equation of a line is *y = -3x + 1*. What is the slope of the line perpendicular to this line?

Accepted Answer

1/3

Answer

-1/3

Answer

-3

Answer

3

Question 49

Which equation represents a line with a slope of -1 and a y-intercept of 5?

Accepted Answer

y = -x + 5

Answer

y = -x - 5

Answer

y = x + 5

Answer

y = x - 5

Question 50

A taxi company charges a flat fee of $5 plus $2 per mile. Write a linear equation to represent the total cost (C) of a taxi ride in terms of the number of miles (m).

Accepted Answer

C = 2m + 5

Answer

C = 5m - 2

Answer

C = 5m + 2

Answer

C = 2m - 5