1. 4.4 Slope Formula

2. Slope can be expressed different ways:
UP or DOWN
RIGHT
A line has a positive slope if it is going uphill from left to right.
A line has a negative slope if it is
going downhill from left to right.

3. Rise
Run 4
THE SLOPE IS 3 4 3
Discuss vertical change

4. Find the slope of the following line.
The slope is… 1 2

5. Find the slope of the line.
The slope is…. -3

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

7. Determine the slope of the line shown.

8. What is the slope of a horizontal line?
The line doesn’t rise!
All horizontal lines have a slope of 0.

9. What is the slope of a vertical line?
The line doesn’t run!
All vertical lines have an undefined slope.

10. Find the slope of these lines.
Black line 3
Red Line 1
Blue Line -1/2
Have students practice.

11. Find the slope of these lines
Orange line = 0
Green Line = Undefined

12. Determining Slope Rise=1 Rise=12 Run =2 Run =4 Rise=6 Run =2 Slope=

13. REMEMBER THE SLOPE FORMULA???!!!!!
Let’s find the slope of a line with two points, WITHOUT LOOKING AT A GRAPH.
REMEMBER THE SLOPE FORMULA???!!!!!

14. 2) Find the slope of the line that passes through the points (-2, -2) and (4, 1).
When given points, it is easier to use the formula!
y2 is the y coordinate of the 2nd ordered pair (y2 = 1)
y1 is the y coordinate of the 1st ordered pair (y1 = -2)

15. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).
x y1
x y2

16. Sample Problems: Find the slope of the line thru the points given:
(-3,-1) and (-2,4)
(-3,4) and (2,-2)
x1 y1
x2 y2
x1 y1
x2 y2

17. Independent Practice: Calculate the slope for each pair of points
Independent Practice: Calculate the slope for each pair of points. Classify each slope as positive, negative, zero, or undefined.
1. (2, 2) and (3, 5)
2. (0, 0) and (3, 0)
Slope: 3 Classification: Positive
Slope: 0
Classification: Horizontal
3. (-2, -1) and (-1, -4)
4. (2, 3) and (2, 7)
Slope: -3
Classification: Negative
Slope: Undefined Classification: Vertical
5. (-1, -1) and (5, 5)
6. (8, 4) and (6, 4)
Slope: 1 Classification: Positive
Slope: 0 Classification: Zero

18. Draw a line through the point (2,0) that has a slope of 3.
1. Graph the ordered pair (2, 0).
2. From (2, 0), apply rise over run (write 3 as a fraction).
3. Plot a point at this location.
4. Draw a straight line through the points. 1 3

19. If you know the slope and one point on the line you can draw the line
If you know the slope and one point on the line you can draw the line. Example: slope is 1/3 and the point (-2,-1)

20. Now you draw a line. Given: slope is 2/3 and the point is (1,0)

21. then tell me the slope of that line after you graphed it.
Graph the line y = 3x +1,
then tell me the slope of that line after you graphed it.
The slope is 3
x y -2 -1 1 2 -5 -2 1 4 7

22. then tell me the slope of that line after you graphed it.
Graph the line 2x + y = 4,
then tell me the slope of that line after you graphed it.
y = -2x + 4
The slope is -2
x y -2 -1 1 2 8 6 4 2

23. then tell me the slope of that line after you graphed it.
Graph the line y = -5,
then tell me the slope of that line after you graphed it.
The slope is 0
x y -2 -1 1 2 -5

24. then tell me the slope of that line after you graphed it.
Graph the line y = 2x,
then tell me the slope of that line after you graphed it.
The slope is 2
x y -2 -1 1 2 -4 -2 2 4

25. then tell me the slope of that line after you graphed it.
Graph the line y = 3x - 2,
then tell me the slope of that line after you graphed it.
The slope is 3
x y -2 -1 1 2 -8 -5 -2 1 4

26. then tell me the slope of that line after you graphed it.
Graph the line 2x + 3y = 6,
then tell me the slope of that line after you graphed it.
The slope is -2/3
x y -6 -3 3 6 6 4 2 -2

27. then tell me the slope of that line after you graphed it.
Graph the line y = -x - 2,
then tell me the slope of that line after you graphed it.
The slope is -1
x y -2 -1 1 2 -1 -2 -3 -4

28. then tell me the slope of that line after you graphed it.
Graph the line 3x – 4y = 12,
then tell me the slope of that line after you graphed it.
The slope is 3/4
x y -8 -4 4 8 -9 -6 -3 3

29. then tell me the slope of that line after you graphed it.
Graph the line x – y = 5,
then tell me the slope of that line after you graphed it.
y = x - 5
The slope is 1
x y -2 -1 1 2 -7 -6 -5 -4 -3

30. To solve this, plug the given information into the formula
The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r.
To solve this, plug the given information into the formula

31. To solve for r, simplify and write as a proportion.
Cross multiply.
1(-4) =
4(4 – r)

32. Simplify and solve the equation. 1(-4) = 4(4 – r)
-20 = -4r
5 = r
The ordered pairs are (5, 6) and (4, 2)