Linear Relationships Review

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is a proportional relationship?

Back

A proportional relationship is a type of linear relationship where the ratio of the two variables remains constant. It can be expressed in the form y = kx, where k is a constant.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0, represented by the term 'b' in the equation y = mx + b.

Front

How can you identify a proportional relationship from an equation?

Back

A proportional relationship can be identified from an equation if it can be written in the form y = kx, where k is a non-zero constant and there is no constant term added or subtracted.

Front

What does it mean if a relationship is non-proportional?

Back

A non-proportional relationship means that the ratio between the two variables is not constant. This often occurs when there is a constant added or subtracted in the equation.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 1?

Back

The equation of the line is y = 2x + 1.

Front

If Joe can make 45 t-shirts every 3 hours, what is his rate of making t-shirts per hour?

Back

Joe's rate is 15 t-shirts per hour (45 t-shirts / 3 hours = 15 t-shirts/hour).

Front

What is the significance of the slope in a real-world context?

Back

In a real-world context, the slope can represent rates such as speed, cost per item, or any other rate of change between two quantities.

Front

How do you determine if a graph represents a proportional relationship?

Back

A graph represents a proportional relationship if it passes through the origin (0,0) and is a straight line.