Multiple Representations of Linear Functions

Front

What does the slope of a linear function represent in a real-world context?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable. For example, in a cost function, it indicates how much the cost increases for each additional unit purchased.

Front

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

Back

Front

How do you find the slope from two points on a line?

Back

Front

What does the y-intercept of a linear function represent?

Back

Front

What is a linear function?

Back

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the significance of the slope in a cost function?

Back

In a cost function, the slope indicates the variable cost per unit, showing how much the total cost increases with each additional unit produced.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases, showing an inverse relationship.

Front

How can you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through these points.

Front

What is the relationship between the slope and the steepness of a line?

Back

The greater the absolute value of the slope, the steeper the line. A slope of 0 indicates a horizontal line, while an undefined slope indicates a vertical line.