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 slope from a table of values?

Back

To determine the slope from a table of values, calculate the change in y divided by the change in x (rise/run) between two points.

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 the value of y when x = 0.

Front

If two linear functions have the same slope, what can be said about their rates of change?

Back

If two linear functions have the same slope, they have the same rate of change.

Front

How can you compare the slopes of two linear equations?

Back

You can compare the slopes of two linear equations by looking at the coefficients of x in their slope-intercept form (y = mx + b). The larger the coefficient, the steeper the slope.

Front

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

Back

A negative slope indicates that as the x-value increases, the y-value decreases. This means the function is decreasing.

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

How do you find the rate of change from a word problem involving costs?

Back

To find the rate of change from a word problem involving costs, identify the fixed costs and the variable costs per unit, then calculate the slope as the variable cost per unit.

Front

What is the significance of the initial fee in a cost function?

Back

The initial fee represents the fixed cost that does not change with the number of units (e.g., guests) and is the y-intercept in the cost function.