WGU OUM2 Tasks 1–4 – Algebra for Secondary Mathematics Teaching – (Passed
Task).
Part 1: Foundations of Algebra – Linear Equations & Functions (Questions 1-35)
Linear Equations & Slope
1. What is the slope of the line passing through the points (2, 5) and (6, 13)?
A. 2
B. 3
C. 4
D. 1/2
Answer: A. 2
Rationale: Slope (m) = (y₂ - y₁)/(x₂ - x₁) = (13 - 5)/(6 - 2) = 8/4 = 2. This concept is
fundamental to understanding rate of change in linear functions .
2. Which form of a linear equation is written as y = mx + b?
A. Standard form
B. Point-slope form
C. Slope-intercept form
,D. Intercept form
Answer: C. Slope-intercept form
Rationale: Slope-intercept form (y = mx + b) is the most intuitive for graphing,
where m represents slope and b represents the y-intercept. This form is essential
for students to quickly identify key features of a line .
3. A line has a slope of -3 and passes through the point (4, 2). What is its equation
in point-slope form?
A. y - 2 = -3(x - 4)
B. y + 2 = -3(x + 4)
C. y - 4 = -3(x - 2)
D. y = -3x + 14
Answer: A. y - 2 = -3(x - 4)
Rationale: Point-slope form is y - y₁ = m(x - x₁). Substituting m = -3, x₁ = 4, and y₁ =
2 gives y - 2 = -3(x - 4). This form is particularly useful when the slope and one
point are known .
,4. What is the x-intercept of the line 3x - 4y = 12?
A. (4, 0)
B. (3, 0)
C. (0, -3)
D. (0, 4)
Answer: A. (4, 0)
Rationale: The x-intercept occurs when y = 0. Substitute y = 0: 3x - 4(0) = 12 → 3x
= 12 → x = 4, giving point (4, 0). Understanding intercepts helps students graph
lines efficiently .
5. Which lines are parallel to y = 2x + 5?
A. y = -2x + 3
B. y = 2x - 7
C. y = 1/2 x + 5
D. y = -1/2 x + 1
Answer: B. y = 2x - 7
, Rationale: Parallel lines have identical slopes. The given line has slope m = 2, so
any line with slope 2 is parallel, regardless of the y-intercept. This is a key concept
when teaching the relationship between slopes of parallel and perpendicular lines
.
6. A line perpendicular to y = 3x - 2 has a slope of:
A. 3
B. -3
C. 1/3
D. -1/3
Answer: D. -1/3
Rationale: Perpendicular lines have slopes that are negative reciprocals. Since the
original slope is 3, the negative reciprocal is -1/3. The product of perpendicular
slopes equals -1: 3 × (-1/3) = -1 .
7. Solve the equation for x: 2(x - 3) + 4x = 5x - 2
A. x = 2
Task).
Part 1: Foundations of Algebra – Linear Equations & Functions (Questions 1-35)
Linear Equations & Slope
1. What is the slope of the line passing through the points (2, 5) and (6, 13)?
A. 2
B. 3
C. 4
D. 1/2
Answer: A. 2
Rationale: Slope (m) = (y₂ - y₁)/(x₂ - x₁) = (13 - 5)/(6 - 2) = 8/4 = 2. This concept is
fundamental to understanding rate of change in linear functions .
2. Which form of a linear equation is written as y = mx + b?
A. Standard form
B. Point-slope form
C. Slope-intercept form
,D. Intercept form
Answer: C. Slope-intercept form
Rationale: Slope-intercept form (y = mx + b) is the most intuitive for graphing,
where m represents slope and b represents the y-intercept. This form is essential
for students to quickly identify key features of a line .
3. A line has a slope of -3 and passes through the point (4, 2). What is its equation
in point-slope form?
A. y - 2 = -3(x - 4)
B. y + 2 = -3(x + 4)
C. y - 4 = -3(x - 2)
D. y = -3x + 14
Answer: A. y - 2 = -3(x - 4)
Rationale: Point-slope form is y - y₁ = m(x - x₁). Substituting m = -3, x₁ = 4, and y₁ =
2 gives y - 2 = -3(x - 4). This form is particularly useful when the slope and one
point are known .
,4. What is the x-intercept of the line 3x - 4y = 12?
A. (4, 0)
B. (3, 0)
C. (0, -3)
D. (0, 4)
Answer: A. (4, 0)
Rationale: The x-intercept occurs when y = 0. Substitute y = 0: 3x - 4(0) = 12 → 3x
= 12 → x = 4, giving point (4, 0). Understanding intercepts helps students graph
lines efficiently .
5. Which lines are parallel to y = 2x + 5?
A. y = -2x + 3
B. y = 2x - 7
C. y = 1/2 x + 5
D. y = -1/2 x + 1
Answer: B. y = 2x - 7
, Rationale: Parallel lines have identical slopes. The given line has slope m = 2, so
any line with slope 2 is parallel, regardless of the y-intercept. This is a key concept
when teaching the relationship between slopes of parallel and perpendicular lines
.
6. A line perpendicular to y = 3x - 2 has a slope of:
A. 3
B. -3
C. 1/3
D. -1/3
Answer: D. -1/3
Rationale: Perpendicular lines have slopes that are negative reciprocals. Since the
original slope is 3, the negative reciprocal is -1/3. The product of perpendicular
slopes equals -1: 3 × (-1/3) = -1 .
7. Solve the equation for x: 2(x - 3) + 4x = 5x - 2
A. x = 2
