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Applications of Linear Graphs

Linear equations in word problems

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Applications of Linear Graphs

Did you know that the United States uses miles to measure distances, while most of the rest of the world uses kilometers? Suppose you were an American visiting Asia, and you were using a graph to convert kilometers to miles to make distances easier to understand. Would you know how to convert a distance such as 10 kilometers? 

Analyzing Linear Graphs

Analyzing linear graphs is a part of life – whether you are trying to decide to buy stock, figure out if your blog readership is increasing, or predict the temperature from a weather report. Although linear graphs can be quite complex, such as a six-month stock graph, many are very basic to analyze.

Let's analyze the given linear graphs to answer to following problems:

  1. The graph below shows the solutions to the price before tax and the price after tax at a particular store. Determine the price after tax of a $6.00 item.

By finding the appropriate \begin{align*}x\end{align*} value ($6.00), you can find the solution, which is the \begin{align*}y\end{align*} value (approximately $6.80). Therefore, the price after tax of a $6.00 item is approximately $6.80.

  1. The following graph shows the linear relationship between Celsius and Fahrenheit temperatures. Using the graph, convert \begin{align*}70^\circ F\end{align*} to Celsius.

By finding the temperature of \begin{align*}70^\circ F\end{align*} and locating its appropriate Celsius value, you can determine that \begin{align*}70^\circ F \approx 22^\circ C\end{align*}.

  1. Use the same graph to convert 30 degrees Celsius to Farenheit.

By finding the temperature of \begin{align*}30^\circ C\end{align*} and locating its appropriate Fahrenheit value, you can determine that \begin{align*}30^\circ C \approx 85^\circ F\end{align*}.


Example 1

Earlier, you were asked how to convert a distance such as 10 kilometers to miles using a graph that displays the conversion between kilometers and miles. 

License: CC BY-NC 3.0

The graph above shows the line that represents the conversion between miles and kilometers with miles on the \begin{align*}x-\end{align*}axis and kilometers on the \begin{align*}y-\end{align*}axis. To convert the distance 10 kilometers to miles, go to the value 10 on the \begin{align*}y-\end{align*}axis and move across until you find the corresponding \begin{align*}x-\end{align*}value one the line. That value will be the number of miles that corresponds to 10 kilometers.

Example 2

Suppose a job pays $20 per hour. A graph of income based on hours worked is shown below. Use the graph to determine how many hours are required to earn $60.

By finding the amount of $60 on the vertical axis, you can follow a horizontal line through the value, until it meets the graph. Follow a vertical line straight down from there, until it meets the horizontal axis. There, the value in hours is 3. This means that the number of hours of work needed to earn $60 is 3 hours.


  1. Using the tax graph from the Concept, determine the net cost of an item costing $8.00 including tax.
  2. Using the temperature graph from the Concept, determine the following:
    1. The Fahrenheit temperature of \begin{align*}0^\circ C\end{align*}
    2. The Celsius temperature of \begin{align*}0^\circ F\end{align*}
    3. The Celsius equivalent to the boiling point of water \begin{align*}(212^\circ F\end{align*})
  3. At the airport, you can change your money from dollars into Euros. The service costs $5, and for every additional dollar you get 0.7 Euros. Make a table for this information and plot the function on a graph. Use your graph to determine how many Euros you would get if you give the exchange office $50.

The graph below shows a conversion chart for converting between the weight in kilograms and the weight in pounds. Use it to convert the following measurements.

  1. 4 kilograms into weight in pounds
  2. 9 kilograms into weight in pounds
  3. 12 pounds into weight in kilograms
  4. 17 pounds into weight in kilograms

Mixed Review

  1. Find the percent of change: An item costing $17 now costs $19.50.
  2. Give an example of an ordered pair located in Quadrant III.
  3. Jodi has \begin{align*}\frac{1}{3}\end{align*} of a pie. Her little brother asks for half of her slice. How much pie does Jodi have?
  4. Solve for \begin{align*}b: b+16=3b-2\end{align*}.
  5. What is 16% of 97?
  6. Cheyenne earned a 73% on an 80-question exam. How many questions did she answer correctly?
  7. List four math verbs.

Review (Answers)

To see the Review answers, open this PDF file and look for section 4.4. 

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Linear Function A linear function is a relation between two variables that produces a straight line when graphed.
Slope Slope is a measure of the steepness of a line. A line can have positive, negative, zero (horizontal), or undefined (vertical) slope. The slope of a line can be found by calculating “rise over run” or “the change in the y over the change in the x.” The symbol for slope is m

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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