Linear Relationships and Equations

This lesson covers linear non-proportional relationships, explaining how they differ from proportional ones by not passing through the origin. It demonstrates how to use equations, tables, and graphs to represent these relationships with real-world examples, such as calculating bowling charges, earnings after transportation costs, water park ticket costs, and tree growth over time. The lesson emphasizes understanding the rate of change and the importance of recognizing non-proportional relationships in various contexts.

What distinguishes a linear non-proportional relationship from a proportional one?

• It cannot be represented by an equation.

• It has a constant rate of change.

• It forms a curve instead of a line.

• It does not pass through the origin.

In the bowling scenario, what does the equation y = 3x + 2 represent?

• The cost of a single game.

• The number of games played.

• The total charge for renting shoes and playing games.

• The cost of renting a bowling lane.

How does the value of y change as x increases in the bowling scenario?

• It remains constant.

• It increases by 3.

• It doubles.

• It decreases by 2.

In the part-time work scenario, what does the equation y = 12x - 4 represent?

• The cost of transportation.

• The number of hours worked.

• The total earnings after transportation costs.

• The total earnings before transportation costs.

What is the rate of change in Frank's earnings per hour?

• $4

• $16

• $8

• $12

In the water park scenario, what does the equation y = 2x + 20 represent?

• The cost of entry only.

• The cost of tickets only.

• The total cost including entry and tickets.

• The number of tickets purchased.

Why is the relationship in the water park scenario not proportional?

• The line does not pass through the origin.

• The equation does not include a constant term.

• The total cost decreases with more tickets.

• The cost per ticket is not constant.

In the tree growth scenario, what does the equation y = 2/5x + 10 represent?

• The initial height of the tree.

• The growth rate of the tree per year.

• The diameter of the tree after x years.

• The number of years the tree has been growing.

Why can the points in the tree growth scenario be connected with a line?

• The tree's diameter decreases over time.

• The tree's growth rate is not constant.

• The tree's growth is measured in whole numbers only.

• The tree grows continuously over time.

What is the significance of the 'b' value in the equation y = mx + b?

• It determines the curvature of the line.

• It shows the x-intercept of the line.

• It indicates the y-intercept of the line.

• It represents the slope of the line.