IDENTIFYING PROPORTIONS
A proportional relationship graph must pass through this special point.
What is the origin (0,0)?
Look at these two proportional relationships. The steeper line represents this type of rate compared to the other line.
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What is a greater (or faster) rate?
All proportional relationships can be written in this standard algebraic equation form using a constant k.
y=?
What is y = kx?
Look at this calculation: 5 apples weigh 0.60 kg, so what is the weight per apple?
What is 0.12 kg?
When you buy gas, the relationship between gallons pumped and total cost is always this type of relationship.
Example: 1 gallon= $3.00, 2 gallons = $6.00, 4 gallons = $12.00
What is a proportional relationship?
The graph of a proportional relationship must be this type of line.
What is a straight line?
This graph shows point (1, 2.5). This coordinate point tells us where the unit rate is located. What is the value of the unit rate?
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What is 2.5?
Andre bikes 1 mile in 5 minutes. If t = time and d = distance, his equation is t = 5d. What equation can he use to find the distance?
What is d=(1/5)* t?
In a proportional table, if 5 bananas = 1.6 pounds, then 3 bananas = ? and 12 bananas = ?. Use the unit rate of 0.32 pounds per banana.
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What are 0.96 pounds and 3.84 pounds?
Andre bikes 1 mile in 5 minutes (rate = 1/5 miles/min).
Kiran walks 1 mile in 15 minutes (rate = 1/15 miles/min).
This person is faster.
Who is Andre?
If a graph is a straight line but doesn't pass through (0,0), the relationship has this property.
What is not proportional?
This graph shows that 6 pounds cost $16.50. Find the cost per pound.
What is $2.75?
A salad dressing recipe calls for 3 tablespoons of oil for every 2 tablespoons of vinegar. This constant of proportionality value represents the tablespoons of oil per tablespoon of vinegar?
What is 1.5 (3/2)?
In a proportional table, when you calculate y/x for each row, you should get the same number. This number is called this.
What is the constant of proportionality?
A smoothie recipe calls for 5 cups strawberries for every 2 cups bananas. If you use 1 cup bananas, you need this many cups of strawberries.
What is 2.5 cups? (5/2 cups of strawberry)
Look at these four graphs from the actual test. Students must identify which graph represents a proportional relationship by checking two requirements.
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What are "straight line" AND "passes through origin"?
Look at this graph showing a proportional relationship. Point (2, 6) is marked. Calculate the value of y when x = 1.
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What is 3?
Students often write d = 15*t and the reciprocal equation as d = (1/15)t when Kiran walks 1 mile in 15 minutes. However, what mistake was made with the equations?
What is switching the variables?
Look at this coordinate plane showing a proportional relationship. The point (4, 12) is marked. After you calculate the unit rate, where do you find that coordinate point on a coordinate plane?
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What is (1,3)?
On a graph, what does this point (1, 2.5) represent?
What is the unit rate?
The equation F = (9/5)C + 32 is NOT proportional because of an extra guest.
What is 32 (or the constant term)?
In proportional relationships, this mathematical concept represents how steep (the slope) of a line is, AND equals the k value in the equation Y=k*X.
What is the constant of proportionality (unit rate)?
Look at this graph showing y = 2x + 3. This equation is NOT proportional because of this special guest?
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What is adding 3 (non-zero y-intercept or non-zero value)?
Look at this banana weight table from the test. Find the unit rate, then calculate the missing weights. If 5 bananas = 1.6 pounds, then 3 bananas weigh how much, and 12 bananas?
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What is 0.96 pounds? (12 bananas = 3.84 pounds)
Look at this equation y = (9/5)x + 32. Calculate: when x = 5, what does y equal and is it proportional?
What is 41? (And NO, it's not proportional because 41 ≠ 0)