Testinar Grade 7 math

Recognizing Proportional Relationships

Students will build Grade 7 mastery of recognizing proportional relationships using models, equations, and test-style reasoning.

CH01-02 Ratios and Proportional Relationships

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Which table shows a proportional relationship between $x$ and $y$?
1. Neither
2. Option B only
3. Both A and B
4. Option A only
A smoothie recipe uses $2$ cups of berries for every $3$ cups of yogurt. If you use $8$ cups of berries, how many cups of yogurt do you need?
1. $10$ cups
2. $16$ cups
3. $14$ cups
4. $12$ cups
Which equation represents a proportional relationship?
1. $y = 3x + 5$
2. $y = 2x + 1$
3. $y = x - 2$
4. $y = 7x$
A car travels at a constant speed. After $2$ hours, it has gone $110$ miles. After $5$ hours, it has gone $275$ miles. Is the distance proportional to time?
1. Cannot determine
2. No
3. Only after 3 hours
4. Yes
Which table does NOT show a proportional relationship?
1. This one (shown above)
2. $y = 6x$
3. A line through $(0,0)$ and $(3,12)$
4. All the above show proportional relationships
A recipe calls for $\frac{1}{2}$ cup of flour for every $\frac{1}{4}$ cup of sugar. Which ratio represents the proportional relationship?
1. $1:2$
2. $1:4$
3. $4:1$
4. $2:1$
The graph of which equation is a straight line passing through the origin?
1. $y = 2x - 3$
2. $y = 0.5x + 2$
3. $y = x + 1$
4. $y = -5x$
Jamal buys notebooks at $3 each. The table below shows his total cost for different numbers of notebooks. Does the table show a proportional relationship?
1. Yes, ratio is $1:3$
2. No, the ratio changes
3. Cannot determine
4. Yes, ratio is $3:1$

Teacher and parent reference

Answer key and explanations

D. Option A only
Check constant $y/x$: A gives $4,4,4,4$ (constant — proportional). B gives $2,2.5,2.33,2.5$ (not constant).
D. $12$ cups
Set up proportion: $\frac{2}{3} = \frac{8}{y}$. Cross multiply: $2y = 24$, so $y = 12$.
D. $y = 7x$
Proportional relationships have form $y = kx$ (passing through origin with no constant term). Only $y = 7x$ fits.
D. Yes
Check the constant-of-proportionality across rows: $\frac{110}{2} = 55$ mph and $\frac{275}{5} = 55$ mph. The ratio is constant, so distance is proportional to time.
D. All the above show proportional relationships
The table has ratio $y/x: 5/1=5, 10/2=5, 15/3=5, 20/4=5$ (constant). Option B: $y=6x$ is proportional. Option C: line through origin $(0,0)$ and $(3,12)$ has slope $4$, so $y=4x$ (proportional). All are proportional.
D. $2:1$
Divide: $\frac{1/2}{1/4} = \frac{1}{2} \times \frac{4}{1} = 2$. For every 1 cup sugar, you need 2 cups flour.
D. $y = -5x$
Proportional equations pass through origin: substitute $x=0$, get $y=0$. Only $y=-5x$ gives $(0,0)$.
D. Yes, ratio is $3:1$
Each row: $6/2=3$, $12/4=3$, $18/6=3$, $24/8=3$. Constant ratio of 3 dollars per notebook.