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Proportional and Linear Relationships
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Proportional and Linear Relationships
Answer each question. Show your reasoning for questions that ask you to explain or solve.
Recognize Relationships
1.A proportional relationship is graphed as a straight line. Through which point must the line pass?
- (0, 0)
- (0, 1)
- (1, 0)
- (1, 1)
2.Which equation describes a proportional relationship?
- y = 4x + 3
- y = 7x
- y = x - 5
- y = -2x + 6
3.For a proportional relationship, the constant of proportionality is the line's .
4.Select every description that represents a function.
- A rule that assigns each input exactly one output
- A vertical line on a coordinate plane
- A table in which input 3 has outputs 5 and 8
- The equation y = 6x - 2
Rates, Tables, and Graphs
5.A straight line passes through the origin and the point (5, 20). What is the unit rate, or change in y for each 1-unit increase in x?
6.Amara models the cost of a radio station sticker pack with y = 3x + 4, where x is the number of extra stickers and y is the total cost in dollars. Is this relationship proportional? Explain using the equation.
7.In the direct variation y = kx, y = 21 when x = 7. Find k.
Songs
2
4
6
Airtime (minutes)
7
14
21
8.Use the song-and-airtime table above. Is airtime proportional to the number of songs? State the constant of proportionality in minutes per song.
9.Line A passes through the intersection of the coordinate axes and the point (4, 12). Line B crosses the y-axis at 2 and passes through (2, 6). Which line shows a proportional relationship? Explain how you can tell.
Solve Linear Systems
10.Find the solution to the system: y = 3x - 2 and y = -x + 10. Give the coordinates where the two lines intersect.
11.At the school radio station, Brianna compares two ways to order music clips. Plan A costs $5 to set up plus $2 per clip, so C = 2n + 5. Plan B costs $11 to set up plus $1 per clip, so C = n + 11. How many clips make the plans cost the same, and what is that shared cost?
12.Match each relationship to its description.
- y = 8x
- y = 8x + 3
- y = -2x
- y = 5
- Proportional relationship with constant of proportionality -2
- Horizontal line with y-intercept 5
- Linear relationship with y-intercept 3
- Proportional relationship with constant of proportionality 8
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