Linear Functions Review

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and can include curves, parabolas, or other shapes.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, representing the point where the line crosses the y-axis.

Front

How do you find the rate of change from two points?

Back

The rate of change can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a pizza costs $15 and each topping costs $1.50, what is the equation representing the total cost?

Back

The equation is y = 1.50x + 15, where y is the total cost and x is the number of toppings.

Front

How can you determine if a function is linear or nonlinear from its equation?

Back

If the equation can be written in the form y = mx + b, it is linear; otherwise, it is nonlinear.

Front

What does it mean if a function has a positive slope?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

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

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.