C 957 | C957 Exam 2: Applied Algebra Updated and
Latest Questions and Correct Answers with
Rationale - WGU
1. Solve the following linear equation for x: 5x - 12 = 18.
A. x = 1.2
B. x = 1.5
C. x = 30
D. x = 6
Correct Answer: D
Explanation: To solve this equation, you must first add 12 to both sides to isolate the
variable term. This calculation results in 5x equaling 30. Following this, you divide both
sides by 5 to find the value of x. The division results in x being equal to 6 exactly. This
systematic approach ensures all operations are balanced on both sides of the equality.
2. Which of the following represents the slope of the line passing through the points (2, 5)
and (4, 13)?
A. m = 2
B. m = 8
C. m = 0.25
D. m = 4
Correct Answer: D
Explanation: The slope is calculated using the formula change in y divided by change in x.
Subtracting the y-coordinates gives 13 minus 5 which equals 8. Subtracting the x-
coordinates gives 4 minus 2 which equals 2. Dividing 8 by 2 results in a slope of 4. This
numerical value represents the constant rate of change between the two given points.
3. Solve the inequality: -3x + 7 < 19.
A. x > -4
B. x < -4
C. x > 4
D. x < 4
Correct Answer: A
,Explanation: First, subtract 7 from both sides to isolate the term with the variable. This
leaves you with negative 3x being less than 12. When dividing by a negative number, the
inequality sign must be reversed. Dividing 12 by negative 3 results in negative 4, so x is
greater than negative 4. Reversing the sign is a critical step often missed in linear inequality
problems.
4. In the linear model y = 25x + 150, which represents a technician’s total fee where x is the
number of hours worked, what does the value 150 represent?
A. The fixed service call fee regardless of hours.
B. The total number of hours worked.
C. The hourly rate charged by the technician.
D. The maximum amount a customer will pay.
Correct Answer: A
Explanation: The value 150 is the y-intercept of the linear equation. In real-world
contexts, the y-intercept represents the initial value or starting point when the
independent variable is zero. Therefore, even if zero hours are worked, the fee starts at 150
dollars. This is commonly referred to as a fixed cost or flat fee in business models. The
hourly rate is instead represented by the slope of 25.
5. Solve the system of equations using substitution: y = 2x and x + y = 12.
A. (6, 6)
B. (4, 8)
C. (8, 4)
D. (3, 9)
Correct Answer: B
Explanation: Start by substituting the expression for y from the first equation into the
second equation. This gives the equation x plus 2x equals 12. Simplifying this results in 3x
equaling 12, which means x equals 4. Substitute x back into the first equation to find that y
equals 2 times 4, which is 8. The ordered pair (4, 8) is the only point that satisfies both
equations.
6. What is the y-intercept of the line defined by the equation 4x - 2y = 10?
A. (0, -5)
B. (0, 5)
C. (2.5, 0)
D. (0, 10)
,Correct Answer: A
Explanation: To find the y-intercept, you must set the value of x to zero in the equation.
This simplifies the equation to negative 2y equals 10. Dividing both sides by negative 2
results in y equaling negative 5. Therefore, the coordinates of the intercept are zero comma
negative 5. This point is where the graph crosses the vertical axis.
7. A gym membership costs $30 per month plus a one-time initiation fee of $50. Which
equation represents the total cost (C) for m months?
A. C = 50m + 30
B. C = 80m
C. C = 30m + 50
D. C = 30 + 50
Correct Answer: C
Explanation: The total cost is determined by a variable monthly fee and a fixed starting
fee. The monthly fee of 30 dollars is multiplied by the number of months m. The one-time
fee of 50 dollars is added once as the y-intercept. This creates the linear function C equals
30m plus 50. This model accurately predicts long-term costs based on membership
duration.
8. If a line is horizontal, what is its slope?
A. 0
B. Undefined
C. 1
D. -1
Correct Answer: A
Explanation: A horizontal line has no change in the y-coordinate as the x-coordinate
increases. Using the slope formula, the numerator becomes zero because the rise is zero.
Zero divided by any non-zero run results in a slope of zero. This indicates that there is no
rate of change in the vertical direction. Consequently, the equation of such a line is always y
equals a constant.
9. Solve for y in the equation: 2(y - 3) = 14.
A. y = 7
B. y = 10
C. y = 8.5
D. y = 4
, Correct Answer: B
Explanation: First, distribute the 2 into the parentheses to get 2y minus 6 equals 14. Add 6
to both sides to move the constant term, resulting in 2y equals 20. Then, divide by 2 to
solve for the variable y. This yields a solution where y equals 10. This ensures that the left
side of the equation balances with the right side.
10. Which graph represents the inequality y >= 2x + 1?
A. A dashed line with shading below.
B. A solid line with shading below.
C. A dashed line with shading above.
D. A solid line with shading above.
Correct Answer: D
Explanation: The ‘greater than or equal to’ symbol indicates a solid line because the values
on the line are included. Shading above the line is required because the inequality specifies
values of y that are greater than the line. A dashed line would only be used for strict
inequalities like ‘greater than’. Checking a point like (0,5) confirms the shading is in the
correct region. Therefore, a solid line with upward shading is the correct graphical
representation.
11. What does it mean if a system of two linear equations has no solution?
A. The lines are the same.
B. The lines intersect at the origin.
C. The lines are parallel.
D. The lines are perpendicular.
Correct Answer: C
Explanation: In a system of linear equations, a solution is defined as a point of
intersection. Parallel lines have the same slope but different y-intercepts, meaning they
never cross. Because they never touch, there is no set of coordinates that satisfies both
equations simultaneously. This condition is known as an inconsistent system. Graphical
evidence would show two distinct lines that maintain a constant distance apart.
12. Convert the equation 3x + y = 9 into slope-intercept form.
A. y = 3x + 9
B. y = -3x + 9
C. x = -1/3y + 3
D. y = -3x - 9
Latest Questions and Correct Answers with
Rationale - WGU
1. Solve the following linear equation for x: 5x - 12 = 18.
A. x = 1.2
B. x = 1.5
C. x = 30
D. x = 6
Correct Answer: D
Explanation: To solve this equation, you must first add 12 to both sides to isolate the
variable term. This calculation results in 5x equaling 30. Following this, you divide both
sides by 5 to find the value of x. The division results in x being equal to 6 exactly. This
systematic approach ensures all operations are balanced on both sides of the equality.
2. Which of the following represents the slope of the line passing through the points (2, 5)
and (4, 13)?
A. m = 2
B. m = 8
C. m = 0.25
D. m = 4
Correct Answer: D
Explanation: The slope is calculated using the formula change in y divided by change in x.
Subtracting the y-coordinates gives 13 minus 5 which equals 8. Subtracting the x-
coordinates gives 4 minus 2 which equals 2. Dividing 8 by 2 results in a slope of 4. This
numerical value represents the constant rate of change between the two given points.
3. Solve the inequality: -3x + 7 < 19.
A. x > -4
B. x < -4
C. x > 4
D. x < 4
Correct Answer: A
,Explanation: First, subtract 7 from both sides to isolate the term with the variable. This
leaves you with negative 3x being less than 12. When dividing by a negative number, the
inequality sign must be reversed. Dividing 12 by negative 3 results in negative 4, so x is
greater than negative 4. Reversing the sign is a critical step often missed in linear inequality
problems.
4. In the linear model y = 25x + 150, which represents a technician’s total fee where x is the
number of hours worked, what does the value 150 represent?
A. The fixed service call fee regardless of hours.
B. The total number of hours worked.
C. The hourly rate charged by the technician.
D. The maximum amount a customer will pay.
Correct Answer: A
Explanation: The value 150 is the y-intercept of the linear equation. In real-world
contexts, the y-intercept represents the initial value or starting point when the
independent variable is zero. Therefore, even if zero hours are worked, the fee starts at 150
dollars. This is commonly referred to as a fixed cost or flat fee in business models. The
hourly rate is instead represented by the slope of 25.
5. Solve the system of equations using substitution: y = 2x and x + y = 12.
A. (6, 6)
B. (4, 8)
C. (8, 4)
D. (3, 9)
Correct Answer: B
Explanation: Start by substituting the expression for y from the first equation into the
second equation. This gives the equation x plus 2x equals 12. Simplifying this results in 3x
equaling 12, which means x equals 4. Substitute x back into the first equation to find that y
equals 2 times 4, which is 8. The ordered pair (4, 8) is the only point that satisfies both
equations.
6. What is the y-intercept of the line defined by the equation 4x - 2y = 10?
A. (0, -5)
B. (0, 5)
C. (2.5, 0)
D. (0, 10)
,Correct Answer: A
Explanation: To find the y-intercept, you must set the value of x to zero in the equation.
This simplifies the equation to negative 2y equals 10. Dividing both sides by negative 2
results in y equaling negative 5. Therefore, the coordinates of the intercept are zero comma
negative 5. This point is where the graph crosses the vertical axis.
7. A gym membership costs $30 per month plus a one-time initiation fee of $50. Which
equation represents the total cost (C) for m months?
A. C = 50m + 30
B. C = 80m
C. C = 30m + 50
D. C = 30 + 50
Correct Answer: C
Explanation: The total cost is determined by a variable monthly fee and a fixed starting
fee. The monthly fee of 30 dollars is multiplied by the number of months m. The one-time
fee of 50 dollars is added once as the y-intercept. This creates the linear function C equals
30m plus 50. This model accurately predicts long-term costs based on membership
duration.
8. If a line is horizontal, what is its slope?
A. 0
B. Undefined
C. 1
D. -1
Correct Answer: A
Explanation: A horizontal line has no change in the y-coordinate as the x-coordinate
increases. Using the slope formula, the numerator becomes zero because the rise is zero.
Zero divided by any non-zero run results in a slope of zero. This indicates that there is no
rate of change in the vertical direction. Consequently, the equation of such a line is always y
equals a constant.
9. Solve for y in the equation: 2(y - 3) = 14.
A. y = 7
B. y = 10
C. y = 8.5
D. y = 4
, Correct Answer: B
Explanation: First, distribute the 2 into the parentheses to get 2y minus 6 equals 14. Add 6
to both sides to move the constant term, resulting in 2y equals 20. Then, divide by 2 to
solve for the variable y. This yields a solution where y equals 10. This ensures that the left
side of the equation balances with the right side.
10. Which graph represents the inequality y >= 2x + 1?
A. A dashed line with shading below.
B. A solid line with shading below.
C. A dashed line with shading above.
D. A solid line with shading above.
Correct Answer: D
Explanation: The ‘greater than or equal to’ symbol indicates a solid line because the values
on the line are included. Shading above the line is required because the inequality specifies
values of y that are greater than the line. A dashed line would only be used for strict
inequalities like ‘greater than’. Checking a point like (0,5) confirms the shading is in the
correct region. Therefore, a solid line with upward shading is the correct graphical
representation.
11. What does it mean if a system of two linear equations has no solution?
A. The lines are the same.
B. The lines intersect at the origin.
C. The lines are parallel.
D. The lines are perpendicular.
Correct Answer: C
Explanation: In a system of linear equations, a solution is defined as a point of
intersection. Parallel lines have the same slope but different y-intercepts, meaning they
never cross. Because they never touch, there is no set of coordinates that satisfies both
equations simultaneously. This condition is known as an inconsistent system. Graphical
evidence would show two distinct lines that maintain a constant distance apart.
12. Convert the equation 3x + y = 9 into slope-intercept form.
A. y = 3x + 9
B. y = -3x + 9
C. x = -1/3y + 3
D. y = -3x - 9
