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 Depdendent Variable

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 Dependent Variable

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# Plotting a Point

If the x-coordinate and the y-coordinate of a point are given, we can plot the point on a Cartesian coordinate system.

Procedure â€” To Plot a Point on a Cartesian Coordinate System

Step 1 Draw (or imagine) a vertical line through the x-coordinate of the point.

Step 2 Draw (or imagine) a horizontal line through the y-coordinate of the point.

Step 3 Place a dot where the lines intersect.

Example 1

Plot the point (3, 7) on a Cartesian coordinate system.

Solution

Step 1 Draw (or imagine) a vertical line through the x-coordinate of the point.

Draw a vertical line through the x-axis at 3.

Step 2 Draw (or imagine) a horizontal line through the y-coordinate of the point.

Draw a horizontal line through the y-axis at 7.

Step 3 Place a dot where the lines intersect.

Example 2

Plot each point on a Cartesian coordinate system.

Solution

Exercise 3

The data in the table represent the total distance traveled by a car in 0 hour, 1 hour, 2 hours, and 3 hours. Plot the data on a Cartesian coordinate system.
 ttime (hours) d distance (miles) 0 0 1 40 2 80 3 120

Solution The data correspond to these points: (0, 0), (1, 40), (2, 80), (3, 120)

To plot these points, we change the way we display the coordinate system.

Horizontal axis:

â€¢ The first column in the data table represents time, so we label the horizontal axis t instead of x.

â€¢ The times are between 0 and 3 hours, so we change the scale of the horizontal axis so each mark represents 0.25 hours.

â€¢ There are no negative times, so we do not show much of the negative horizontal axis.

Vertical axis:

â€¢ The second column in the data table represents distance, so we label the vertical axis with the letter d instead of y.

â€¢ Since the distances range from 0 to 120 miles we change the scale of the vertical axis so that each mark represents 10 miles.

â€¢ There are no negative distances, so we do not show much of the negative vertical axis. The four points are plotted on the graph.