Bowling Costs and Linear Relationships

Mr. Reeves introduces linear non-proportional relationships, contrasting them with proportional ones. Using Jake's bowling problem, he explains how costs differ for Jake and Aaron, illustrating proportional and non-proportional relationships. Aaron's costs form a proportional relationship, while Jake's costs, due to shoe rental, form a non-proportional relationship. Graphs and equations are used to demonstrate these concepts, highlighting the differences in their mathematical representations.

What is the main focus of the lesson introduced by Mr. Reeves?

• Proportional relationships

• Quadratic relationships

• Linear non-proportional relationships

• Non-linear relationships

In Jake's Ballistic Bowling problem, what does the variable 'x' represent?

• Number of players

• Cost of renting shoes

• Number of games played

• Total cost

What is the equation representing Aaron's bowling costs?

• y = 3x

• y = 2x

• y = x + 3

• y = 3x + 2

Why is Aaron's bowling cost considered a proportional relationship?

• Because it includes a fixed cost

• Because it is non-linear

• Because it has a slope of 2

• Because y divided by x is constant

What additional cost does Jake incur that Aaron does not?

• Shoe rental fee

• Membership fee

• Cost per game

• Parking fee

What is the equation representing Jake's bowling costs?

• y = x + 2

• y = 3x

• y = 2x + 3

• y = 3x + 2

How do the lines representing Aaron's and Jake's costs compare on a graph?

• They intersect at the origin

• They overlap completely

• They are parallel

• They are perpendicular

What does the 'b' in the equation y = mx + b represent?

• The x-intercept

• The slope of the line

• The y-intercept

• The constant of proportionality

What is a key characteristic of a linear non-proportional relationship?

• It has a constant y divided by x

• It forms a straight line but does not pass through the origin

• It passes through the origin

• It is always non-linear

What is the difference between 'm' and 'k' in the context of linear equations?

• 'm' is used for non-proportional relationships, 'k' for proportional

• 'm' is always greater than 'k'

• 'm' and 'k' are interchangeable

• 'm' is used for quadratic equations