High School

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**Setting Up Graphs**

Please be sure to show **all of your work** when solving each of the following problems (i.e., show your calculations for your x- and y-axes scales).

1. Set up a graph (but do not plot points yet) using the following table of values:

Theo operates a lawn mowing company. The following table of values represents the time Theo expects to spend mowing lawns of various sizes.

| Area (m²) | Time (minutes) |
|-----------|----------------|
| 100 | 20 |
| 200 | 25 |
| 300 | 30 |
| 400 | 35 |
| 500 | 40 |
| 600 | 45 |
| 700 | 50 |

(a) What is the dependent variable?

(b) What is the independent variable?

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To set up your graph, ensure that you have correctly labeled your axes and have chosen an appropriate scale for both the area (m²) and time (minutes).

**Note:** The dependent variable is typically plotted on the y-axis, while the independent variable is plotted on the x-axis. Check your graph setup to ensure accuracy.

Answer :

To set up your graph based on the provided table of values, you need to correctly identify and label the axes, determine appropriate scales, and consider the relationship between the variables.


  1. Identify the Variables:


    • Dependent Variable: Time (minutes). Typically, the dependent variable is what is measured or observed. In this context, the time it takes Theo to mow lawns of different sizes is what's being measured, so it goes on the y-axis.

    • Independent Variable: Area ([tex]m^2[/tex]). Usually, the independent variable is what you manipulate or control, in this case, the size of the lawn, so it goes on the x-axis.



  2. Determine the Scales:


    • X-axis (Area [tex](m^2)[/tex]):


      • Determine the range of your x-values (100 to 700).

      • Choose increments that allow for easy plotting and adequate spacing. A scale of 100 units per interval can be a good choice, allowing you to mark every 100 units on the x-axis up to at least 700.



    • Y-axis (Time (minutes)):


      • Determine the range of your y-values (20 to 50).

      • Choose increments for the y-axis. A scale of 5 units per interval will allow you adequate spacing and clarity, marking every 5 units up to 50.





  3. Setting Up the Graph:


    • Draw two perpendicular lines to represent the x-axis and y-axis.

    • Label the x-axis as "Area [tex](m^2)[/tex]" and the y-axis as "Time (minutes)".

    • Mark and label the axes with the respective scales you've set.

    • Ensure that both axes begin at zero and extend to the maximum value needed to include all data points.




Now, your graph is correctly set up to plot the points from the given data. Make sure there is enough space between each axis label for clarity and readability when you eventually plot the points.

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Rewritten by : Barada