Line Graphs

Learning Outcomes

  • Construct a line graph

Recall: COORDINATE PLANE

The intersecting x- and y-axes of the coordinate plane divide it into four sections. These four sections are called quadrants. Quadrants are named using the Roman numerals I, II, III, and IV, beginning with the top right quadrant and moving counter clockwise.

The rectangular coordinate system

A graph with an x-axis running horizontally and a y-axis running vertically. The location where these axes cross is labeled the origin, and is the point zero, zero. The axes also divide the graph into four equal quadrants. The top right area is quadrant one. The top left area is quadrant two. The bottom left area is quadrant three. The bottom right area is quadrant four.

Recall: Plotting Points

A point (also called an ordered pair) has two values: “The first value is called the x-coordinate and the second value is the y-coordinate.”

The ordered pair x y is labeled with the first coordinate x labeled as

To plot a point, you go along the x-axis and find the value of the x-coordinate and then go along the y-axis and find the value of the y-coordinate.

Let’s try locating the point [latex]\left(2,5\right)[/latex]. In this ordered pair, the [latex]x[/latex]-coordinate is [latex]2[/latex] and the [latex]y[/latex]-coordinate is [latex]5[/latex].

We start by locating the [latex]x[/latex] value, [latex]2[/latex], on the [latex]x\text{-axis.}[/latex] Then we lightly sketch a vertical line through [latex]x=2[/latex], as shown in the image below.

The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. There is a vertical dotted line passing through 2 on the x-axis.
Now we locate the [latex]y[/latex] value, [latex]5[/latex], on the [latex]y[/latex] -axis and sketch a horizontal line through [latex]y=5[/latex]. The point where these two lines meet is the point with coordinates [latex]\left(2,5\right)[/latex]. We plot the point there, as shown in the image below.

The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. An arrow starts at the end of the first arrow at 2 on the x-axis and goes vertically 5 units to a point labeled

Reminder: Any ordered pair, such as (2,5), represents one single point on the graph.

Another type of graph that is useful for specific data values is a line graph. In the particular line graph shown in the next example, the x-axis (horizontal axis) consists of data values and the y-axis (vertical axis) consists of frequency points. The frequency points are connected using line segments.

Example

In a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his or her chores. The results are shown in the table and figure below.

Number of times teenager is reminded Frequency
0 2
1 5
2 8
3 14
4 7
5 4

 

A line graph showing the number of times a teenager needs to be reminded to do chores on the x-axis and frequency on the y-axis.

Try It

In a survey, 40 people were asked how many times per year they had their car in the shop for repairs. The results are shown in the table below. Construct a line graph.

Number of times in shop Frequency
0 7
1 10
2 14
3 9