7.3 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 a table of values?

Back

To find the slope from a table of values, select two points (x1, y1) and (x2, y2) and use the formula: slope (m) = (y2 - y1) / (x2 - x1).

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.

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How can you compare the slopes of two linear functions?

Back

To compare the slopes, identify the slope (m) from the equations of both functions. The function with the greater slope has a greater rate of change.

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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, meaning they increase or decrease at the same rate.

Front

How do you determine which service is cheaper using linear equations?

Back

To determine which service is cheaper, calculate the total cost for the same number of items (e.g., movies) using the equations and compare the results.

Front

What is the formula for calculating the total cost in a linear function?

Back

The total cost can be calculated using the formula: Total Cost = (Rate per item * Number of items) + Initial fee.

Front

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

Back

The initial fee is a fixed cost that must be paid regardless of the number of items. It affects the total cost but does not change with the quantity.

Front

How can you visually compare two linear functions on a graph?

Back

You can visually compare two linear functions by plotting their graphs on the same coordinate plane and observing their slopes and y-intercepts.