Calculating Slope

Now that you are very familiar with points and their coordinates, we will explore lines in a coordinate plane.

Sometimes a line can be drawn through two or more points. The “steepness” or “slant” of the line is called its “slope”.

The slope of a line can be positive (the line goes “uphill” from left to right),

or negative (the line goes “downhill” from left to right).

The slope of line is represented by a number.

Visit the Syracuse University’s math tutorial site called “Calculating the Slope” (http://syllabus.syr.edu/cid/graph/

Unit4a.html). Carefully read through the lesson and examples. Click the “Practice” and “Additional Practice” buttons to try some problems on your own. Click on the “View detailed Solution” buttons as needed.

Now that you are an expert on slope, complete the following:

1. How many points are needed to be able to calculate the slope of a line?

2. Write the formula for slope in the blank:

3. If two lines are drawn on the same coordinate plane, the steeper of the two lines will have the slope.

4. Find the slopes of the lines that contain these points:

a. (4, 5) and (2, 1)

b. (4, 5) and (-2, -1)

c. (-4, -5) and (2, 1)

d. (-4, -5) and (-2, -1)

5. What do you notice about the slopes of the lines in problems “b” and “c” above?

How can this be true when the points are not the same?

6. What is the relationship between the slopes of the lines in “a” and “d” in problem #4?

Why is this true?

7. Tell if the slopes of the lines containing the following points are positive or negative. (You do not need to calculate the slope.)

a. (-2, 3) and (2, 15)

b. (-4, 5) and (3, -7)

c. (7, 5) and (3, 1)

8. Explain how you solved the problems in #7 above.

9. Find the slopes of the lines that contain these points:

a. (2, -1) and (5, -7)

b. (5, 3) and (-3, -1)

c. (6, 9) and (8, 3)

d. (-2, -6) and (-5, -3)