1. Introduction
To Slope

2. OBJECTIVE: The students will be able to find the slope of a line given 2 points and a graph.

3. What is the meaning of this sign?
Icy Road Ahead
Steep Road Ahead
Curvy Road Ahead
Trucks Entering Highway Ahead

4. Slope is a
measure of
Steepness.

5. Types of Slope
Zero
Negative
Positive
Undefined or
No Slope

6. Slope is sometimes referred to as the “rate of change” between 2 points. The rate of change must be constant

7. Determine the slope of the line.
When given the graph, it is easier to apply “rise over run”.

8. Example 1: Determine the slope of the line
Start with the lower point and count how much you rise and run to get to the other point!
rise 3 = = 6
run 6 3
Notice the slope is positive AND the line increases!

9. used to represent slope.
The letter “m” is
used to represent slope.
Why?

10. If given 2 points on
a line, you may find
the slope using the
formula m = y2 – y1
x2 – x1

11. The formula may
sometimes be written
as m =∆y . ∆x
What is ∆ ?
Change

12. Example 3: Find the slope of the line through the points (3, 7) and (5, 19).y1 x2 y2
m = 19 – 7
5 – 3
m = 12 2
m = 6

13. Example 4: Find the slope of the line through (-3, 2) and (-6, -2)
-6 – (-3)
m = -4 -3
m = 4 3

14. This means there is ZERO SLOPE= a horizontal line.
What if the numerator is 0?
0 # = 0
This means there is ZERO SLOPE= a horizontal line.

15. This means there is NO SLOPE= a vertical line.
What if the denominator is 0?
# 0 = undefined
This means there is NO SLOPE= a vertical line.

16. If given an equation
of a line, there are
2 ways to find the
slope and y-intercept.

17. One method is to write the equation in slope-intercept form,
which is y = mx + b.
slope
y-intercept

18. y = 3x + ½ Find the slope and y-intercept of the following equations.

19. First, solve the equation for y.
3x + 5y = 10
First, solve the equation for y.
3x + 5y = 10
5y = -3x + 10
y = -3/5 x + 2
m= -3/5
b = 2

20. The End