Linear Functions

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 does the slope of a linear function 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 function?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the function on the y-axis.

Front

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

Back

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

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

If a linear function has a slope of 0, what does that indicate about the graph?

Back

A slope of 0 indicates that the graph is a horizontal line, meaning the y-value does not change as x changes.

Front

What is the difference between a linear and a nonlinear function?

Back

A linear function graphs to a straight line, while a nonlinear function graphs to a curve.

Front

Write the linear function for a scenario where a person earns $15 per hour and has a starting salary of $200.

Back

The function can be written as E(x) = 15x + 200, where E is the earnings after x hours.

Front

How do you find the cost function for a service that charges a flat fee plus a variable rate?

Back

The cost function can be expressed as C(x) = fixed fee + (variable rate * x), where x is the quantity of service.