Algebra 2 Chapter 3 Quiz
Questions: 16 · 10 minutes
1. Which system has two different lines that are parallel?
The lines y = 2x + 1 and y = −2x + 1, which have opposite slopes
The lines y = 4x − 5 and y = −4x − 5, which share a y-intercept
The lines y = 4x + 1 and y = −4x + 5, which have different slopes and intercepts
The lines y = 4x + 1 and y = 4x − 5, which have equal slopes but different intercepts
2. Two delivery services charge according to y = 15x + 20 and y = 15x + 5, where x is the number of miles. What does the graph show about when their total charges are equal?
They are never equal because the lines have the same slope and different intercepts.
They are equal at 15 miles.
They are equal only at 0 miles.
They are equal at 1 mile.
3. A club pays a fixed $40 setup fee plus $8 per shirt, modeled by y = 8x + 40. It sells each shirt for $12, modeled by y = 12x. At what point do the cost and revenue graphs intersect?
(5, 60)
(8, 104)
(10, 80)
(10, 120)
4. A line crosses the y-axis at 4 and passes through the point (2, 0). Which equation represents it?
y equals negative 2 times x, plus 4
y equals 2 times x, plus 4
y equals negative x, plus 2
y equals 2 times x, minus 4
5. The lines y = 2x − 3 and y = −x + 6 are graphed on the same coordinate plane. Where do they intersect?
The point with coordinates x = 1 and y = 5
The point with coordinates x = 3 and y = 6
The point with coordinates x = 3 and y = 3
The point with coordinates x = −3 and y = −9
6. Adult tickets cost $12, student tickets cost $8, and 30 tickets bring in $280. If a is the number of adult tickets and s is the number of student tickets, which system models the situation?
a + s = 30 and 8a + 12s = 280
a + s = 280 and 12a + 8s = 30
a + s = 30 and 12a + 8s = 280
12a + 8s = 30 and a − s = 280
7. A shop can display no more than 40 notebooks and planners altogether and must display at least 10 notebooks. If x is the number of notebooks and y is the number of planners, which set of constraints models the display?
The total is at least 40, notebooks are at most 10, and both quantities are nonnegative.
The total is at most 40, notebooks are at least 10, and both quantities are nonnegative.
The total equals 40, planners are at least 10, and both quantities are nonnegative.
The total is at most 10, notebooks are at least 40, and both quantities are nonnegative.
8. Which graph description correctly represents x + y ≤ 6 and x ≥ 1?
Dashed boundaries, shaded above x + y = 6 and left of x = 1
A solid line for x + y = 6, a dashed line for x = 1, and shading above both
Solid boundaries, with the overlap on or below x + y = 6 and on or right of x = 1
Solid boundaries, with the overlap on or above x + y = 6 and on or left of x = 1
9. How should the system y = −3x + 2 and 6x + 2y = 4 be classified?
It has no solution because the lines are parallel.
It has exactly one solution at (0, 4).
It has infinitely many solutions because both equations describe the same line.
It has exactly one solution at (2, −4).
10. Which pair of equations represents the same line and therefore has infinitely many solutions?
y = 2x + 3 and 2y = 4x − 3
2x + y = 6 and y = −2x + 6
3x − y = 6 and y = −3x + 6
x + y = 4 and y = x + 4
11. Which point satisfies both inequalities y ≥ x and y < 3?
(2, 2)
(1, 3)
(−1, −2)
(3, 2)
12. On a graph of two linear equations, what does an intersection point represent?
Any point located between the two lines
The y-intercept shared by both coordinate axes
The average slope of the two lines
An ordered pair that satisfies both equations
13. Compared with y = x + 1, how is the graph of y = x − 3 positioned?
It is shifted 2 units to the right.
It is shifted 4 units downward.
It is reflected across the x-axis.
It is rotated because its slope changes.
14. Which description matches the graph of y > −2x + 5?
A solid boundary line with shading below it
A solid boundary line with shading above it
A dashed boundary line with shading below it
A dashed boundary line with shading above it
15. At what point do the boundary lines y = x + 2 and y = −x intersect?
(1, −1), where the first coordinate is positive
(−1, 1), where both equations have a value of 1
(−2, 0), the x-intercept of y = x + 2
(0, 2), the y-intercept of y = x + 2
16. A student graphs x + y = 5 and y = x − 1. Which point should appear as the intersection?
(3, 2)
(2, 1)
(2, 3)
(4, 1)