A linear function is a function with a constant rate of change. In a linear function, the x-values change by a constant amount and the y-values change by a constant amount.

One way that you can represent a linear function is called slope-intercept form.

y equals mx plus b, or slope-intercept form of a linear function

When you have a situation with a starting point, or initial condition, and a constant rate of change, you can frequently represent that situation using a linear function in slope-intercept form.

You may also see situations that result in equations written in standard form. Standard form of a linear equation is Ax + By = C. In this representation, A, B, and C are constants that show the relationship between two variables, x and y.

standard form of a linear function with constants explained

Interactive exercise. Assistance may be required. Now, you are going to practice writing equations when given a verbal description. Drag the matching equation under the appropriate label. When you have completed the matching, copy or print the page into your notebook.


When writing the equations in slope-intercept form, how did you determine the coefficient for the variable?

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The coefficient is the rate of change presented in the situation.Close Pop Up

When writing the equations in slope-intercept form, how did you determine the addend, or the value of b?

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The addend, or the value of b, is the starting point, or initial value, in the situation.Close Pop Up

When writing the equations in standard form, how did you determine the coefficients for each of the variables?

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A rate, or multiplier, that relates to the number of items described by a variable becomes the coefficient for that variable. Close Pop Up

Practice

  1. Mr. Nguyen is planning a trip to the county fair. The fair charges a $10 parking fee, and admission tickets cost $7 per person. Write an equation that describes the relationship between c, the total cost to attend the fair, if Mr. Nguyen purchases tickets for p people.

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    Which rate depends on the number of people, and which fee is the same regardless of the number of people? Close Pop Up

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    c = 10 + 7p Close Pop Up
  2. Ruben took a taxi from his hotel to the airport. The taxi company charged a $3.60 meter start fee and $1.60 per mile. Ruben spent $26 for the taxi ride, not including tip. Write an equation that could be used to determine n, the number of miles from Ruben’s hotel to the airport.
    taxi

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    Which rate depends on the number of miles, and which fee is the same regardless of the number of miles? Close Pop Up

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    26 = 3.6 + 1.6m Close Pop Up
  3. Jordyn bought a sweater that was on sale for 20% off the regular price. Write an equation that describes the relationship between r, the regular price of the jacket, and the sale price s.

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    When you are taking a discounted price, what operations do you need to consider? Close Pop Up

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    s = r – 0.2r    OR    s = 0.8r Close Pop Up
  4. Mrs. Banks is saving for a vacation for her family. She has deposited $350 in a savings account and will add $50 to the account each month. Write an equation that describes the relationship between a, the amount of money Mrs. Banks will have in the account after m months.
    two people in a car in front of a palm tree

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    Which rate depends on the number of months, and which amount is the same regardless of the number of months? Close Pop Up

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    a = 350 + 50m Close Pop Up
  5. Brent mixes two types of coffee beans to create his favorite type of coffee. Costa Rica Delight beans cost $12.50 per pound, and Ethiopian Special beans cost $9.25 per pound. Write an equation that Brent can use to determine the number of pounds of Costa Rica Delight beans, c, and Ethiopian Special beans, e, he can use to make a mixture that costs $32.

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    Use the cost per pound as a multiplier for each variable. Close Pop Up

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    Check Your Answer

    12.50c + 9.25e = 32 Close Pop Up