Proportional Relationships and Unit Rates

Mr. Buffington's lesson covers proportional relationships using graphs and fractions. It explains how to identify proportional relationships on graphs, calculate unit rates, and solve equations for missing values. The lesson includes practical applications and sample questions to reinforce understanding. Advanced problem-solving techniques are also discussed, highlighting the advantages of using equations over graphs for accuracy and flexibility.

What are the two key indicators of a proportional relationship on a graph?

• The line is straight and does not pass through the origin.

• The line is curved and passes through the origin.

• The line is curved and does not pass through the origin.

• The line is straight and passes through the origin.

If 1 pound of gumdrops costs $2, what is the cost for 0.5 pounds?

• $1.00

• $0.50

• $1.50

• $2.00

How can you find the unit rate if it's not given?

• Multiply the cost by the number of pounds.

• Divide the number of pounds by the cost.

• Divide the cost by the number of pounds.

• Add the cost and the number of pounds.

What is the equation to find the y-value in a proportional relationship?

• y = K + x

• y = K - x

• y = K * x

• y = K / x

If the constant of proportionality is 2, what is the cost for 1.5 pounds of gumdrops?

• $5.00

• $3.00

• $2.00

• $4.00

What is the equation for x in terms of y and the constant of proportionality?

• x = y * K

• x = y - K

• x = y / K

• x = y + K

If the constant of proportionality is 8, what is the equation for y?

• y = 8 + x

• y = 8 * x

• y = 8 / x

• y = 8 - x

What is the unit rate if the distance is 8 kilometers in 1 hour?

• 10 km/h

• 8 km/h

• 6 km/h

• 4 km/h

How far would you travel in 7 and 1/3 hours if the unit rate is 8 km/h?

• 56 km

• 58 and 2/3 km

• 60 km

• 62 km

What is a key advantage of using equations over graphs?

• Equations are less accurate.

• Equations provide more accuracy and flexibility.

• Equations are harder to interpret.

• Equations are limited by paper size.