8.AF.7 Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

How do you determine the rate of change from a table of values?

Back

To determine the rate of change from a table, calculate the difference in y-values divided by the difference in x-values between two points.

Front

What is the y-intercept in a linear function?

Back

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

Front

If a linear function has a slope of 0, what does that mean?

Back

A slope of 0 means that the function is constant; the y-value does not change as the x-value changes.

Front

How can you compare the rates of change of two linear functions?

Back

You can compare the rates of change by looking at the slopes of the functions. The function with the greater slope has a greater rate of change.

Front

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

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they have the same rate of change, but they may have different y-intercepts.

Front

How do you find the cost of a service given a linear equation?

Back

To find the cost of a service, substitute the number of units (e.g., movies) into the linear equation to calculate the total cost.

Front

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

Back

The coefficients in a linear equation indicate the slope and the y-intercept, which determine the line's steepness and position on the graph.