Exploring Algebraic Relationships and Representations

This video tutorial reviews algebraic relationships through multiple representations, focusing on solving equations and graphing. It covers calculating total costs, graphing relationships, understanding multiplicative factors, and identifying equations that represent real-world situations. The tutorial uses examples like DVD purchases, washcloth packaging, and a balloon game to illustrate these concepts.

What is the correct value of R when Q is 5, based on the equation R = Q + 10.1?

• 10.6

• 10.1

• 15.1

• 15.6

What is the value of R when Q is 7, according to the equation R = Q + 10.1?

• 15.3

• 17.1

• 17.2

• 18.1

Which equation correctly represents the total cost T for D DVDs, each costing $15?

• T = 15 + D

• T = D/15

• T = 15D

• T = D + 15

For the equation T = 15D, what is the total cost if 3 DVDs are purchased?

• $45

• $30

• $15

• $60

Which graph correctly represents the equation Y = 4X?

• Graph D

• Graph C

• Graph A

• Graph B

In the equation Y = 4X, what is the value of Y when X is 3?

• 9

• 7

• 4

• 12

If X is 2 and Y is 3, what factor must X be multiplied by to equal Y?

• 1.0

• 1.5

• 2.5

• 2.0

If X is 6 and the factor is 1.5, what is the value of Y?

• 9.5

• 9

• 12

• 6

Which scenario is correctly represented by the equation Y = 74X?

• A restaurant prepares Y batches of sauce from 74 pounds of tomatoes, with each batch weighing X pounds.

• A restaurant serves Y meals, with 74 in the first hour and X in subsequent hours.

• A company uses Y gallons of water at a rate of 74 gallons per hour for X hours.

• A company manufactures 74 glasses per hour, with X clear and Y blue glasses.

Which equation does not represent a linear relationship?

• Y = 74X

• Y = X + 74

• Y = 74 / X

• Y = X * 74