Modeling Linear Relationships

Front

What is the rate of change in a linear relationship?

Back

The rate of change in a linear relationship is the ratio of the change in the dependent variable to the change in the independent variable, often represented as 'rise over run'.

Front

How do you calculate the cost per unit in a linear relationship?

Back

To calculate the cost per unit, divide the total cost by the number of units. For example, if the cost is $110 for 100 units, the cost per unit is $110/100 = $1.10.

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

If a taxi charges $0.30 per mile and has a base fare of $1, what is the equation for the total cost?

Back

The equation for the total cost is y = 0.3x + 1, where y is the total cost and x is the number of miles.

Front

How do you determine the rate of change from a graph?

Back

To determine the rate of change from a graph, select two points on the line, calculate the difference in the y-values (rise) and the difference in the x-values (run), and then divide rise by run.

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.

Front

What does it mean if the rate of change is constant?

Back

If the rate of change is constant, it means that for every unit increase in the independent variable, the dependent variable increases by a fixed amount.

Front

How can you represent a linear relationship using a table?

Back

A linear relationship can be represented using a table by listing pairs of values for the independent and dependent variables that maintain a constant rate of change.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of the dependent variable when the independent variable is zero; it represents the starting point of the relationship.