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

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

Yoko’s Auto and Body Shop uses a table like the one shown to determine how much to charge for labor.

• What is the y-intercept in this situation?

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  (0, 65)

• What does the y-intercept represent in this situation?

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  The fixed service charge, regardless of the amount of time spent on the vehicle repair, is $65.

After reviewing the accounts, Yoko decides that he needs to increase the fixed service charge. Dwayne, his business partner, has prepared the tables below for Yoko to review. Match each table with the description of the y-intercept by dragging the description to the space next to the table.

Pause and Reflect

How can you identify the y-intercept in a table if one of the ordered pairs in the table is not (0, y)? Interactive popup. Assistance may be required.

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Use the ordered pairs in the table to look for a constant rate of change, and then use that rate of change as the slope along with one point from the table to determine the equation of the line in slope-intercept, or y = mx + b, form.

Of the three plans presented by Dwayne, which plan would yield the greatest increase in labor charges?Interactive popup. Assistance may be required.

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The initial service fee is $65. Increasing the service fee by 25% increases the service fee by $16.25, which is less than both $20 and $25. The $25 increase yields the greatest increase in labor charges.

Practice

Use the table below to answer questions 1 through 3.

Sam receives $25 for his birthday.  Instead of spending the money, he decides to put the money in a savings account.  Each week, he deposits $2 into the account. 

1. If Sam combined the $25 birthday gift with $10 from his mother, what would be the new y-intercept in this situation?

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   What is the initial y-intercept?
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   The new y-intercept will be (0, 35).
2. What would the new y-intercept, with the combination of the $25 birthday gift and $10 from Sam’s mother, mean in the context of this situation?

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   What do the x and y variables represent in this situation?
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   At the beginning of Sam’s savings, he will have $35 instead of $25.
3. Sam’s mother offered him 30% of his birthday gift or $10 as a matching deposit for his savings account. Which would increase the y-intercept of this situation more?

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   How much is 30% of $25?
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   The 30% matching deposit is $7.50, which is less than $10. The $10 matching deposit will increase the y-intercept more than the 30% matching deposit.