Exploring Linear Nonproportional Relationships

This video tutorial covers the representation of linear equations, focusing on both proportional and non-proportional relationships. It explains how to graph these equations using ordered pairs and tables of values. The tutorial also delves into solving word problems by setting up equations in slope-intercept form and analyzing graphs to determine linearity. Key concepts such as slope, y-intercept, and constant rate of change are discussed, with examples provided to illustrate these ideas.

What is the main difference between a proportional and a non-proportional linear relationship?

• Proportional relationships have a constant rate of change.

• Non-proportional relationships have a constant rate of change.

• Non-proportional relationships pass through the origin (0,0).

• Proportional relationships pass through the origin (0,0).

Which form is used to represent the equation of a proportional relationship?

• y = kx + b

• y = mx

• y = mx + b

• y = kx + c

In a proportional relationship, what is the y-value when x = 2 for the equation y = 3x?

• 12

• 9

• 6

• 3

What additional value is added in the equation of a non-proportional relationship?

• m

• k

• b

• c

For the equation y = 3x + 2, what is the y-value when x = 3?

• 11

• 8

• 9

• 5

In the word problem about the plant, what does the value of 5 represent in the equation y = 2x + 5?

• The unit rate

• The initial height of the plant

• The number of days

• The slope

What is the slope in the equation y = 3/4x + 4?

• 3/4

• 4

• 1/4

• 3

In the pizza problem, what does the variable 'n' represent?

• Unit rate

• Initial cost

• Number of toppings

• Total cost

What is the total cost of a pizza with 2 toppings if the base cost is $10 and each topping costs $2?

• $18

• $16

• $14

• $12

Why is the relationship between the number of toppings and the total cost of the pizza not proportional?

• The number of toppings is not constant.

• The total cost does not start at zero.

• The cost of toppings varies.

• The total cost is not linear.