Linear Relationships

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 described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) 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 one-unit increase in x.

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What is a proportional relationship?

Back

A proportional relationship is a specific type of linear relationship that passes through the origin (0,0) and can be represented by the equation y = kx, where k is a constant.

Front

How can you represent linear relationships?

Back

Linear relationships can be represented using verbal descriptions, equations, graphs, and tables.

Front

What is the equation for a proportional relationship?

Back

The equation for a proportional relationship is y = kx, where k is the constant of proportionality.

Front

If Sally earns $30 for every 5 hours she babysits, what is her hourly rate?

Back

Her hourly rate is $6 per hour, which can be represented by the equation y = 6x.

Front

What does it mean if a linear equation does not pass through the origin?

Back

If a linear equation does not pass through the origin, it indicates that there is a fixed cost or starting value (y-intercept) when x is 0.

Front

What is the equation for Johnny's carnival expenses?

Back

The equation for Johnny's carnival expenses is y = 2x + 7, where x is the number of tickets and y is the total cost.

Front

What does it mean for a relationship to be linear?

Back

A relationship is linear if it can be represented by a straight line on a graph, indicating a constant rate of change.