Testinar Grade 6 math

Graphing Ratios

Students will build Grade 6 mastery of graphing ratios using models, equations, and test-style reasoning.

CH01-06 Ratios, Rates, and Percents

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

The coordinate plane shows ordered pairs representing the ratio of hours worked to dollars earned. Based on the graph, how much is earned per hour?
1. $$1$ per hour
2. $$5$ per hour
3. $$10$ per hour
4. $$20$ per hour
A ratio table shows the relationship between hours and miles traveled at a constant speed. Which graph correctly represents the data from this table? Looking at the coordinate plane below, which set of points matches this ratio?
1. $(1,1), (2,2), (3,3)$
2. $(1,2), (2,4), (3,6)$
3. $(1,5), (2,7), (3,9)$
4. $(1,3), (2,6), (3,9)$
A store sells oranges at a constant rate. The graph below shows the relationship between the number of oranges and the total cost in dollars. What is the unit rate (cost per orange)?
1. $$0.25$ per orange
2. $$2.00$ per orange
3. $$1.00$ per orange
4. $$0.50$ per orange
This table shows the relationship between gallons of water used and plants watered at a greenhouse. If this relationship is graphed with gallons on the x-axis and plants on the y-axis, what does the point $(1, 4)$ represent?
1. 1 gallon waters 4 plants
2. 4 gallons water 1 plant
3. 1 plant needs 4 gallons
4. 4 gallons water 4 plants
A student created this ratio table about babysitting rates: If the student plots $(0, 0)$, $(2, 24)$, $(4, 48)$, and $(6, 72)$ on a coordinate plane, which statement about the points is true?
1. The points form a vertical line
2. The points form a diagonal line through the origin
3. The points form a horizontal line
4. The points do not form a straight line
Which scenario best matches the graph showing hours on the x-axis and total distance in kilometers on the y-axis?
1. Traveling at 2 km per hour
2. Traveling at 4 km per hour
3. Traveling at 6 km per hour
4. Traveling at 8 km per hour
A recipe uses a 3:2 ratio of flour to sugar. The graph below shows ordered pairs of this ratio. Which point should also be plotted to continue this ratio pattern?
1. $(4, 3)$
2. $(9, 6)$
3. $(5, 4)$
4. $(8, 5)$
The graph shows the relationship between minutes studied and test score points earned. What is the unit rate (points per minute)?
1. $0.25$ points per minute
2. $0.5$ points per minute
3. $1$ point per minute
4. $2$ points per minute

Teacher and parent reference

Answer key and explanations

C. $$10$ per hour
Look at the y-axis label: each tick on the dollars axis stands for $10. The point $(1,1)$ means $1$ hour and $1\times10=$10$, so the rate is $$10$ per hour.
A. $(1,1), (2,2), (3,3)$
The vertical axis is scaled in groups of $50$ miles. So $50$ miles is shown as $1$, $100$ miles as $2$, and $150$ miles as $3$, giving the points $(1,1)$, $(2,2)$, and $(3,3)$.
D. $$0.50$ per orange
At the point where oranges $= 2$, cost $= $1$, giving a ratio of $$1 \div 2 = $0.50$ per orange. Or use any point: at $(8, 4)$, the rate is $$4 \div 8 = $0.50$ per orange.
A. 1 gallon waters 4 plants
On the graph with gallons on the x-axis and plants on the y-axis, the point $(1, 4)$ means 1 gallon (x-value) corresponds to 4 plants watered (y-value). This shows the unit rate: 4 plants per gallon.
B. The points form a diagonal line through the origin
All these points lie on a straight line passing through $(0, 0)$ because the ratio is constant ($12$ dollars per hour). Proportional relationships always graph as straight lines through the origin.
A. Traveling at 2 km per hour
Using two points on the line, e.g., $(1,2)$ and $(2,4)$: slope $=\frac{4-2}{2-1}=2$ km/hr. Verify with $(4,8)$: $8\div 4=2$ km/hr. The constant rate is $2$ km per hour.
B. $(9, 6)$
The ratio is 3:2 (flour:sugar). Points on this line satisfy $\text{sugar} = \frac{2}{3} \times \text{flour}$. Check: $(3, 2)$ gives $2 = \frac{2}{3}(3)$ ✓; $(6, 4)$ gives $4 = \frac{2}{3}(6)$ ✓; $(9, 6)$ gives $6 = \frac{2}{3}(9)$ ✓. The other options do not maintain this ratio.
B. $0.5$ points per minute
Using the point $(2, 1)$: unit rate $= 1 \div 2 = 0.5$ points per minute. Or from $(10, 5)$: unit rate $= 5 \div 10 = 0.5$ points per minute.