Lesson 1

In Share 2 you should have noticed that each graph is a straight line, resulting in a linear relation.

 

The graph you constructed in Try This 1 should have resembled the following graph:

 

 

Notice that the graph is a straight line passing through the origin (0, 0), making it a direct linear relation.

 

The graph you constructed in Try This 2 should have resembled the following graph:

 

 

Notice that the graph results in a straight line that does not pass through the origin, or (0, 0). This is called a partial linear relation. The point where the graph touches or cuts the y-axis is called the y-intercept.

 

In each of the graphs, the rate of change remains constant. Recall from a previous math course that the rate of change for a straight line is also referred to as the slope of the line. The slope compares the variables x and y, meaning that the change in the dependent variable (y) is proportional to the change in the independent variable (x).

 

For example, the table shows that for every 8-h increase in the number of hours worked (independent variable, or x), the amount of money made (dependent variable, or y) increases by 144.

 

Number of Hours Worked	Amount of Money Made
0	0
8	144
16	288
24	432
32	576
40	720

 

Try This 3

 

Open Partial and Direct Relations and adjust the sliders to respond to the following questions.

 

1. What characteristics of the graph can be changed for the direct linear relation?
2. What characteristics of the graph can be changed for the partial linear relation?
3. What effect on the line does changing the y-intercept have?
4. What effect on the line does changing the slope have?

Save your responses in your course folder.