Meaning of Slope

Sima Javaheri&

Sara Kelly

California Content Standard

• 3.3 Graph linear functions, noting that the vertical change (change in y- value) per unit of horizontal change (change in x- value) is always the same and know that the ratio ("rise over run") is called the slope of a graph.

NCTM Standard

• Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules

Objectives of the Lesson

• Given a graph of a line, students will be able to identify the slope as being positive, negative, zero, or neither.

• Given a graph of a line, students will be able to calculate slope by using rise over run.

• Given a two points on a line, students will be able to apply the slope formula accurately.

What is Slope???

Slope is the ratio of the vertical change to the horizontal change. In a linear relationship, it is a constant rate of change. It can also be characterized as the steepness of a line.

12

12

run

rise

change horizontal

change vertical m slope

xx

yy

Positive vs. Negative Slopes

• A line that moves upward from left to right has a positive slope.

Hint: If you can transform the line to resemble a “P” then it is positive!

• A line that moves downward from left to right has a negative slope.

Hint: If you can transform the line to resemble a “N” then it is negative!

Kinds of Slopes

• Positive Slope

• Negative Slope

Zero and Neither Slope

A line that is flat from left to right has a zero slope.

A line that is straight up and down (vertical) has no slope (neither).

Continued

• Zero

• Neither

Rise over Run

Slope =run

rise

Rise Rise is the vertical distance between the pointsis the vertical distance between the points

RunRun is the horizontal distance between the is the horizontal distance between the pointspoints

Use Rise over Run

•What is the rise What is the rise value?value? Rise = 4Rise = 4

•What is the run What is the run value?value? Run = 1Run = 1

What is the Slope?

41

4

run

rise

Slope Formula

• Given two points and , the slope can be calculated by substituting the x- and y-values into the following formula:

),( 11 yx ),( 22 yx

12

12

xx

yym

Example

Find the slope of the line that goesFind the slope of the line that goes through these two points (1, 1) and (2,3):through these two points (1, 1) and (2,3):

21

2

12

13

m

Now, you try…

Given (0,4) and (2, -2), computeGiven (0,4) and (2, -2), compute the slope using the slope formula:the slope using the slope formula:

32

6

02

42

m

References

1. Kaplan, Andrew. Math On Call. Wilmington: Houghton Mifflin, 1998.

1. Van de Walle, J, & Lovin, L, Teaching Student Centered Mathematics, Boston: Pearson (2001).

2. http://www.math.iupui.edu/~momran/m119/notes/slope.jpg