Master Linear Equations: Conquer One-Variable Equations with Confidence

Question 1

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

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

2x + 3y = 6

Answer

x = 2y + 3

Question 2

Identify the equation with the greatest y-intercept:

Accepted Answer

y = 2x + 6

Answer

y = -3x + 5

Answer

y = 4x - 2

Answer

y = -5x + 1

Question 3

Which of the following systems of equations has infinitely many solutions?

Accepted Answer

3x + y = 6
y = x + 3

Answer

2x - y = 4
y = 2x + 2

Answer

x + 2y = 5
2x + 4y = 10

Answer

3x - y = 6
y = -3x + 3

Question 4

Which equation represents the slope-intercept form of a linear equation?

Accepted Answer

y = mx + b

Answer

y - y1 = m(x - x1)

Answer

x = mx + b

Answer

y = mx - b

Question 5

Which equation represents a line passing through (0, 3) with a slope of 2?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

2x + y = 3

Answer

x - 2y = 3

Question 6

What is the slope of the line described by the equation y = (1/2)x + 2?

Accepted Answer

1/2

Answer

0

Answer

2

Answer

Undefined

Question 7

Find the equation of the line that goes through the point (0, 0) and has a slope of -3.

Accepted Answer

y = -3x

Answer

y = 3x

Answer

x = -3y

Question 8

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

Accepted Answer

-2

Answer

2

Answer

-3

Answer

3

Question 9

A car rental company charges a monthly fee of $15 plus $0.25 per mile driven. Write the equation that represents the total cost of renting the car.

Accepted Answer

y = 15 + 0.25x

Answer

y = 0.25x + 15

Answer

y = 15x + 0.25

Answer

y = 0.25 + 15x

Question 10

Which of the following equations is in the form of a linear equation (with one variable)?

Accepted Answer

2x - 5 = 10

Answer

x + y = 5

Answer

x^2 - 4 = 0

Answer

sin(x) = 0.5

Question 11

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

Accepted Answer

2

Answer

-2

Answer

5

Answer

-5

Question 12

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

Accepted Answer

5

Answer

2

Answer

-2

Answer

-5

Question 13

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

Accepted Answer

y = 2

Answer

y = 2x

Answer

y = -x + 2

Answer

y = x^2

Question 14

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

Accepted Answer

y = -2x + 2

Answer

y = 2x - 2

Answer

y = 2x + 2

Answer

y = -2x - 2

Question 15

Solve for x: 2x + 5 = 11

Accepted Answer

x = 3

Answer

x = 2

Answer

x = 4

Answer

x = 5

Question 16

Determine the slope of the line that passes through points (1, 3) and (4, 7).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 17

Write 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 18

Find the x-intercept of the line: y = 4x - 8.

Accepted Answer

2

Answer

4

Answer

6

Answer

8

Question 19

Solve for y in the equation: 2x - 5y = 10

Accepted Answer

y = (2x - 10)/5

Answer

y = 5(2x - 10)

Answer

y = 10/(2x - 5)

Answer

y = 5/(2x - 10)

Question 20

Which of the following is a necessary step in solving a linear equation?

Accepted Answer

Isolating the variable

Answer

Combining like terms

Answer

Multiplying or dividing by zero

Answer

Factoring

Question 21

Which definition of a linear equation is most accurate?

Accepted Answer

An equation with a constant rate of change

Answer

An equation with only one variable

Answer

An equation that can be graphed as a straight line

Answer

An equation that has a y-intercept and a slope

Question 22

If a linear equation has a slope of -2 and a y-intercept of 3, what is its equation?

Accepted Answer

y = -2x + 3

Answer

y = 3x - 2

Answer

x = -2y + 3

Answer

x = 3y - 2

Question 23

Which of the following is NOT a step involved in solving linear equations?

Accepted Answer

Factoring the equation

Answer

Combining like terms

Answer

Isolating the variable

Answer

Multiplying both sides by the same variable

Question 24

What is the slope of the line passing through (2, 4) and (4, 10)?

Accepted Answer

3

Answer

2

Answer

6

Answer

8

Question 25

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

Accepted Answer

y = 1/2x + 2.5

Answer

y = -1/2x + 4.5

Answer

y = 2x + 1

Answer

y = -2x + 5

Question 26

Which of the following equations represents a linear equation in one variable, y?

Accepted Answer

y = 2x + 3

Answer

y = x^2 + 2

Answer

y = |x| - 1

Answer

y = e^x

Question 27

Solve the system of linear equations: x + y = 5, x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Question 28

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

Accepted Answer

y = -3x + 2

Answer

y = 3x + 2

Answer

y = -3x - 2

Answer

y = 3x - 2

Question 29

Translate the statement "Five less than twice a number is greater than 10" into a linear inequality.

Accepted Answer

2x - 5 > 10

Answer

2x - 5 < 10

Answer

10 - 2x > 5

Answer

10 - 2x < 5

Question 30

Find the solutions to the absolute value inequality: |x + 2| < 4

Accepted Answer

x > -2 and x < 6

Answer

x < -6 or x > 2

Answer

x > -6 and x < 2

Answer

x < -2 or x > 6

Question 31

Which of the following is NOT a way to write a linear equation?

Accepted Answer

Parabolic form

Answer

Slope-intercept form

Answer

Point-slope form

Answer

Standard form

Question 32

Find the slope of the line passing through the points (2, 5) and (4, 9)

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 33

Which equation is linear in one variable, ?

Accepted Answer

2x + 3 = 7

Answer

x * y = 12

Answer

log(x) = y

Answer

x^2 + y = 5

Question 34

Which equation correctly 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 35

Solve the system of equations: x + y = 5, x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 1, y = 4

Answer

x = 4, y = 1

Answer

x = 2, y = 3

Question 36

Which of the following is the equation of a line parallel to the x-axis?

Accepted Answer

y = 5

Answer

y = -x

Answer

y = 2x

Answer

y = x

Question 37

Which of the following inequalities represents the statement "The sum of x and 5 is greater than or equal to 10"?

Accepted Answer

x + 5 ≥ 10

Answer

x - 5 ≤ 10

Answer

x + 5 ≤ 10

Answer

x - 5 ≥ 10

Question 38

The area of a rectangle is 24 square units. If the length of the rectangle is 6 units, what is its width?

Accepted Answer

4 units

Answer

8 units

Answer

12 units

Answer

2 units

Question 39

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

Accepted Answer

-2

Answer

-3

Answer

3

Answer

2

Question 40

What is the *x*-coordinate of the point where the line *y* = 2*x* + 1 crosses the *y*-axis?

Accepted Answer

0

Answer

1

Answer

2

Answer

-1

Question 41

What is the solution to the equation 3x + 5 = 14?

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 1

Answer

x = 6

Question 42

Which equation 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 43

A taxi charges a flat fee of $5 plus $2 per mile. Which equation shows the total cost (C) of a taxi ride based on the number of miles (m)?

Accepted Answer

C = 2m + 5

Answer

C = 2m - 5

Answer

C = 7m

Answer

C = 5m + 2

Question 44

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Accepted Answer

2

Answer

1/2

Answer

-1/2

Answer

-2

Question 45

Solve the equation: 2(x - 3) = 4x + 6

Accepted Answer

x = -3

Answer

x = 3

Answer

x = 6

Answer

x = -6

Question 46

What is the slope of the line with the equation y = -1/2x + 4?

Accepted Answer

-1/2

Answer

-4

Answer

1/2

Answer

4

Question 47

If a line has a slope of 0, what does that tell us about the line?

Accepted Answer

The line is horizontal.

Answer

The line has a y-intercept of 0.

Answer

The line is vertical.

Answer

The line passes through the origin.