7.7A Representing 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, where the change in one variable is proportional to the change in the other.

Front

What does the slope of a line represent in a linear relationship?

Back

The slope of a line represents the rate of change between the two variables in a linear relationship, indicating how much one variable changes for a unit change in the other variable.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the dependent variable when the independent variable is zero.

Front

How can you determine if a relationship is proportional from a graph?

Back

A relationship is proportional if the graph passes through the origin (0,0) and is a straight line, indicating a constant ratio between the two variables.

Front

What is the formula for a linear equation in slope-intercept form?

Back

The formula for a linear equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a non-proportional relationship look like on a graph?

Back

A non-proportional relationship does not pass through the origin and may have a y-intercept that is not zero, indicating that there is an initial value when the independent variable is zero.

Front

How do you calculate the remaining balance in a checking account after multiple purchases?

Back

To calculate the remaining balance, subtract the total amount spent (cost per item multiplied by the number of items purchased) from the initial balance.

Front

What is the significance of the initial fee in a linear relationship?

Back

The initial fee represents a fixed cost that is incurred before any variable costs are added, affecting the overall cost structure of the relationship.

Front

How can you identify points that lie on a line in a graph?

Back

Points that lie on a line satisfy the linear equation of that line, meaning they can be plugged into the equation to yield a true statement.

Front

What is the difference between a proportional and a non-proportional relationship?

Back

A proportional relationship has a constant ratio and passes through the origin, while a non-proportional relationship has a variable ratio and does not pass through the origin.