Proportional vs Non-Proportional Relationships in 8th Grade Math

The video tutorial explains the differences between proportional and non-proportional relationships. It covers how to identify proportional relationships using equations, word problems, graphs, and tables. Proportional relationships are characterized by a constant ratio (y/x) and can be represented by the equation y = kx, with no y-intercept. Non-proportional relationships include a y-intercept or do not maintain a constant ratio. The tutorial provides examples to help determine if a relationship is proportional or non-proportional.

What does the constant 'k' in the equation y = kx represent?

• The y-intercept

• A variable coefficient

• The slope of the line

• A constant ratio of y over x

How can you tell if an equation represents a proportional relationship?

• It can be written in the form y = kx.

• It has a constant addition to x.

• It has a y-intercept other than zero.

• It includes an exponent on the x.

In the equation y = mx + b, what condition makes it represent a non-proportional relationship?

• When y is divided by x

• When m is not equal to 1

• When x is squared

• When b is not equal to 0

Which scenario describes a non-proportional relationship?

• Earning $10 for every book read, starting from the first book.

• Selling lemonade at $2 per cup, with no setup fee.

• A $50 deposit plus $30 per hour for consulting services.

• Charging $15 per hour for tutoring, with no initial fee.

What makes a relationship non-proportional in a word problem?

• Having a constant rate of change

• Having a starting value other than zero

• Only involving addition or subtraction

• Describing a linear relationship

Which example is a proportional relationship?

• A taxi fare that includes a flat booking fee plus a charge per mile

• A gym membership with a monthly fee regardless of usage

• Buying bulk candy at a constant price per pound

• A phone plan with a base fee plus an additional charge per gigabyte of data used

What is true about the graph of a proportional relationship?

• It is a curve that does not pass through the origin.

• It is a straight line that passes through the origin.

• It can be any shape as long as it has a constant slope.

• It is a straight line with a y-intercept not equal to zero.

Why is a graph that doesn't pass through the origin considered non-proportional?

• Because it indicates a variable slope

• Because it doesn't have a constant ratio of y over x

• Because it suggests a constant y-intercept

• Because it means there is a starting value other than zero

In a table representing a proportional relationship, what must be true about the ratio of y over x?

• It varies depending on the value of x.

• It remains constant throughout the table.

• It is always equal to the y-intercept.

• It decreases as x increases.

What indicates a proportional relationship in a table of values?

• The difference between consecutive y-values is constant.

• The ratio of y to x is different for each pair of values.

• The sum of x and y values is constant.

• The ratio of y to x is constant across all pairs of values.