Understanding Unit Rates and Slopes

Answer explanation

The equation y = 5x indicates that the cost per ticket (unit rate) is 5 dollars, as y represents the total cost for x tickets. Therefore, the correct answer is 5.

Tags

CCSS.7.RP.A.2D

Answer explanation

The slope of a line is calculated as the change in y divided by the change in x. Here, the change in y is 8 - 0 = 8 and the change in x is 4 - 0 = 4. Thus, the slope is 8/4 = 2, which is the correct answer.

Tags

CCSS.8.EE.B.5

Table A shows: | x | y | |---|---| | 1 | 3 | | 2 | 6 | | 3 | 9 | Table B shows: | x | y | |---|---| | 1 | 4 | | 2 | 8 | | 3 | 12 | Which relationship has the greater unit rate?

• Table A

• Table B

• Both have the same unit rate

• Cannot be determined

Answer explanation

To find the unit rate, divide y by x for each table. Table A: 3/1 = 3, 6/2 = 3, 9/3 = 3. Table B: 4/1 = 4, 8/2 = 4, 12/3 = 4. Table B has a greater unit rate of 4 compared to Table A's 3.

Tags

CCSS.6.RP.A.3B

• The graph

• Both have the same unit rate

• Cannot be determined

Answer explanation

The equation y = 7x has a unit rate of 7, while the line through (0,0) and (1,5) has a unit rate of 5. Therefore, y = 7x has the greater unit rate.

Tags

CCSS.7.RP.A.2D

If a recipe uses 2 cups of sugar for every 5 cups of flour, what is the unit rate of sugar per cup of flour?

Answer explanation

To find the unit rate of sugar per cup of flour, divide the amount of sugar (2 cups) by the amount of flour (5 cups). This gives \( \frac{2}{5} \), which is the correct answer.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Answer explanation

To find the slope (m) between points (x1, y1) = (2, 6) and (x2, y2) = (4, 12), use the formula m = (y2 - y1) / (x2 - x1). Thus, m = (12 - 6) / (4 - 2) = 6 / 2 = 3. The correct answer is 3.

Tags

CCSS.8.EE.B.5

Answer explanation

The equation y = 9x represents a proportional relationship because it can be expressed as y = kx, where the unit rate (k) is 9. The other options do not have a constant ratio between y and x.

Tags

CCSS.7.RP.A.2C

Answer explanation

To find the price per apple, divide the total price by the number of apples: 6.00 / 12 = 0.50. Therefore, the price per apple is 0.50.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

• Relationship 1

• Relationship 2

• Both have the same unit rate

• Cannot be determined

Answer explanation

To find the unit rates, for Relationship 1, the unit rate is 4 (since y = 4x). For Relationship 2, the unit rate is 6 (y/x = 6/1, 12/2, 18/3). Relationship 2 has the greater unit rate of 6.

Tags

CCSS.6.RP.A.3A

What was Brian's unit rate?

• 15 word per minute
• 30 minutes per word
• 60 minutes per word
• 30 words per minute

Tags

CCSS.7.RP.A.2D