REGENTS-ALGEBRA Linear Equations & Functions 2 — Questions and Answers
Question 1: Which equation is written in standard form?
- y = 3x + 2
- 3x - y = 2 (Correct answer)
- y - 2 = 3(x - 1)
- m = 3, b = 2
Correct answer: 3x - y = 2
Standard form is Ax + By = C; 3x - y = 2 fits this format.
Question 2: A function f is defined by f(x) = 5x - 3. What is f(4)?
- 17 (Correct answer)
- 20
- 23
- 32
Correct answer: 17
f(4) = 5(4) - 3 = 20 - 3 = 17.
Question 3: What is the slope of a line perpendicular to y = (1/3)x + 4?
- 3
- -3 (Correct answer)
- 1/3
- -1/3
Correct answer: -3
Perpendicular slopes are negative reciprocals; the negative reciprocal of 1/3 is -3.
Question 4: James earns $12 per hour. Which equation models his total earnings E after h hours?
- E = h + 12
- E = 12h (Correct answer)
- E = 12/h
- h = 12E
Correct answer: E = 12h
Total earnings equal the hourly rate multiplied by hours worked: E = 12h.
Question 5: Which point lies on the line y = -x + 6?
- (2, 3)
- (3, 3) (Correct answer)
- (4, 2)
- (5, 1)
Correct answer: (3, 3)
Substituting x = 3: y = -3 + 6 = 3, so (3, 3) satisfies the equation.
Question 6: What is the rate of change of the linear function represented by the table: x: 1, 2, 3, 4 and y: 5, 8, 11, 14?
- 2
- 3 (Correct answer)
- 4
- 5
Correct answer: 3
Each time x increases by 1, y increases by 3, so the rate of change (slope) is 3.
Question 7: The equation of a line passing through (0, -4) with slope 2 is:
- y = -4x + 2
- y = 2x + 4
- y = 2x - 4 (Correct answer)
- y = -2x - 4
Correct answer: y = 2x - 4
The point (0, -4) is the y-intercept (b = -4) and slope m = 2, giving y = 2x - 4.
REGENTS-ALGEBRA Linear Equations & Functions 2
Which equation is written in standard form?