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 find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

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 there is no change in the y-value as the x-value changes.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

How can you determine which of two linear functions is cheaper at a given point?

Back

To determine which function is cheaper, compare the y-values (costs) of both functions at the same x-value (input). The function with the lower y-value is cheaper.

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope of the function. It describes how much the output (y) changes for a unit change in the input (x).

Front

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

Back

To compare the rates of change, look at the slopes of the functions. The function with the greater slope has a greater rate of change.