CHSPE Algebra 3 — Questions and Answers
Question 1: Which of the following is the equation of a line with slope -½ and y-intercept 4?
- y = -½x - 4
- y = 4x - ½
- y = -½x + 4 (Correct answer)
- y = ½x + 4
Correct answer: y = -½x + 4
Slope-intercept form y = mx + b with m = -½ and b = 4 gives y = -½x + 4.
Question 2: Solve the system: x + y = 7 and x - y = 3. What is x?
- 2
- 5 (Correct answer)
- 4
- 3
Correct answer: 5
Adding the equations gives 2x = 10, so x = 5.
Question 3: Which expression is equivalent to (2x³)(3x²)?
- 5x⁵
- 6x⁶
- 6x⁵ (Correct answer)
- 5x⁶
Correct answer: 6x⁵
Multiply coefficients (2 × 3 = 6) and add exponents (3 + 2 = 5) to get 6x⁵.
Question 4: A rectangle has a length that is 3 more than twice its width. If the perimeter is 48, what is the width?
- 7 (Correct answer)
- 9
- 11
- 6
Correct answer: 7
Let w = width; 2(2w + 3) + 2w = 48 → 6w + 6 = 48 → w = 7.
Question 5: What is the y-intercept of the line 4x - 2y = 12?
- 6
- -6 (Correct answer)
- 3
- -3
Correct answer: -6
Solve for y: -2y = -4x + 12 → y = 2x - 6, so the y-intercept is -6.
Question 6: If a varies directly with b, and a = 15 when b = 5, what is a when b = 9?
- 3
- 45
- 27 (Correct answer)
- 25
Correct answer: 27
The constant of variation k = 15/5 = 3, so a = 3(9) = 27.
Question 7: Which of the following is NOT a function?
- y = x²
- y = 3x + 1
- x = y² (Correct answer)
- y = |x|
Correct answer: x = y²
x = y² fails the vertical line test since one x maps to two y values (e.g., x = 4 gives y = ±2).
CHSPE Algebra 3
Which of the following is the equation of a line with slope -½ and y-intercept 4?