4.5 Comparing Functions

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the ratio of the change in the dependent variable (y) to the change in the independent variable (x), often represented as 'm' in the slope-intercept form y = mx + b.

Front

How do you determine which service is cheaper based on linear equations?

Back

To determine which service is cheaper, compare the total costs calculated from the linear equations for the same quantity of service (e.g., number of movies). The service with the lower total cost is cheaper.

Front

What is the slope of a line, and how does it relate to rate of change?

Back

The slope of a line is a measure of its steepness and is calculated as the rise over run (change in y over change in x). It represents the rate of change of the dependent variable with respect to the independent variable.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept in a linear equation (y = mx + b) represents the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How can you find the equation of a line given a point and the slope?

Back

You can use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Front

What is a set-up fee in a service context?

Back

A set-up fee is a one-time charge that a company may impose to initiate a service, separate from ongoing costs.

Front

How do you compare two linear functions graphically?

Back

To compare two linear functions graphically, plot both lines on the same coordinate plane and analyze their slopes and y-intercepts to determine which function is greater at specific points.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation indicate the rate of change (slope) and the constant term (y-intercept), which together define the behavior of the function.

Front

How do you calculate the total cost from a linear equation?

Back

To calculate the total cost from a linear equation, substitute the quantity of service (x) into the equation and solve for y, which represents the total cost.

Front

What does it mean if two linear functions have the same rate of change?

Back

If two linear functions have the same rate of change, they are parallel lines, meaning they increase or decrease at the same rate but may have different y-intercepts.