You can also use a table of values to interpret and make predictions about the changes in the slopes of linear functions.

For example, an electrician charges a fixed service fee plus an hourly rate for labor, in addition to the cost of the parts for the electrical repair.

Miguel’s Electric Company uses a table like the one shown to determine how much to charge for labor.

• What is the slope in this situation?

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  45

• What does the slope represent in this situation?

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  The hourly rate for labor is $45 per hour.

After reviewing the accounts, Miguel decides that he needs to increase the hourly rate for labor. Angelica, his business partner, has prepared the tables below for Miguel to review. Match each table with the description of the change in slope by dragging the description to the space next to the table.

Pause and Reflect

How can you identify the slope in a table if the interval in the x-values is not constant?

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For each pair of corresponding values, determine the change in y and the change in x. If the data can be modeled with a linear function, these ratios will all be equivalent.

Of the three plans Angelica presented, which plan would yield the greatest increase in labor charges?

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The initial hourly labor rate is $45. Increasing the hourly labor rate by 20% increases the service fee by $9, which is greater than $5 but less than $15. The $15 increase yields the greatest increase in labor charges.

Practice

Hallie walked her neighbor’s dog each day this summer and saved all the money she earned. Now that school has started, she has begun to withdraw money each week to pay for gasoline for her car.

Use this information to answer Questions 1 through 3.

1. At what rate is Hallie withdrawing money from her savings?

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   What is the slope of the data in the table?
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   Hallie is withdrawing $15 per week.
2. If gasoline prices increase, Hallie must spend more money each week on gasoline for her car. If Hallie spends $20 each week, how will that affect the rate of change in this situation?

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   What would be the new rate of change in this situation?
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   The rate of change will increase by $5 each week.
3. Hallie spends 30% more than she originally planned on gasoline each week. If she withdraws that amount of money from her savings each week, what will be the new rate of withdrawal from Hallie’s savings?

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   What is 30% of the original rate of change?
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   $19.50 per week