Proportional Relationships and Unit Rates

Mrs. Lopez teaches Grade 8 students about representing proportional relationships with equations, focusing on the equation y = kx. She explains the constant of proportionality and how to calculate it by dividing y by x. The lesson includes a practical example comparing corn prices at two stands, using unit rates to determine the better price. Students learn to write equations for each stand and complete tables with calculated values. The lesson concludes with an analysis of bulk purchase benefits, emphasizing the importance of unit rates in decision-making.

What is the general form of the equation used to represent proportional relationships?

• y = mx + b

• y = x + k

• y = kx

• y = x/k

How do you calculate the unit rate to determine the better price for corn?

• Multiply the total cost by the number of ears of corn

• Add the total cost to the number of ears of corn

• Subtract the number of ears of corn from the total cost

• Divide the total cost by the number of ears of corn

In the equation y = kx, what does the variable 'k' represent?

• The total cost

• The number of ears of corn

• The constant of proportionality

• The difference in cost

What is the equation for Alz's produce stand if the constant of proportionality is 0.25?

• d = 0.50x

• d = 0.24x

• d = 0.25x

• d = 0.75x

What is the equation for Barbara's produce stand if the constant of proportionality is 0.24?

• d = 0.75x

• d = 0.50x

• d = 0.24x

• d = 0.25x

If 6 ears of corn cost $1.50 at Alz's stand, what is the cost for 14 ears?

• $3.50

• $3.00

• $4.50

• $4.00

If 13 ears of corn cost $3.12 at Barbara's stand, what is the cost for 21 ears?

• $4.04

• $6.04

• $5.04

• $5.40

How many ears of corn can you buy for $50 at Alz's stand?

• 250

• 200

• 150

• 100

How many ears of corn can you buy for $50 at Barbara's stand?

• 220

• 180

• 200

• 208

Which produce stand offers a better deal for bulk purchases?

• Alz's stand

• Neither

• Barbara's stand

• Both are the same