1. I was clear on everything from the past lessons, except…
FIRE UP!!
FRIDAY
Muddiest Point….
What concept(s) on over the last 2 classes and your last quiz were you unsure about? On the ½ sheet of paper, finish this sentence….
I was clear on everything from the past lessons, except…

2. Linear Function Review
Sections 2-2, 2-3, 2-4
Pages

3. Objectives I can find slope by these methods:
Between 2 points
From a graph (rise over run)
I can graph a linear line using slope and y-intercept
I can manually graph points
I can write an equation for a linear line

4. Slope – The BIG Picture
The slope of a line is the steepness of the line. Slope can be positive, negative, zero, or undefined.
We use the little letter (m) to represent slope in an equation
y= mx + b

5. 4 Types of Slope Positive Negative No Slope Undefined Slope
See examples next slides

6. y-axis Positive Slope m > 0 x-axis Goes UP a Mountain 1 2 6 3 4 5 78 9 10
x-axis
y-axis -2 -6 -3 -4 -5 -7 -8 -9 -1
Positive Slope
m > 0
Goes UP a Mountain

7. y-axis Goes DOWN a Mountain x-axis Negative Slope m < 0 1 2 6 3 4 57 8 9 10
x-axis
y-axis -2 -6 -3 -4 -5 -7 -8 -9 -1
Goes DOWN a Mountain
Negative Slope
m < 0

8. y-axis Horizontal Line x-axis Zero Slope m = 0 1 2 6 3 4 5 7 8 9 10 -2-2 -6 -3 -4 -5 -7 -8 -9 -1
Horizontal Line
Zero Slope
m = 0

9. y-axis Vertical Line x-axis Undefined Slope m = #/0 1 2 6 3 4 5 7 8 910
x-axis
y-axis -2 -6 -3 -4 -5 -7 -8 -9 -1
Vertical Line
Undefined Slope
m = #/0

10. Real World Slope Problems
What REAL World things would not work correctly without slope?

11. Ramps for Various Purposes

12. The Roof on Buildings

13. Decking & Roads

14. Slope
Slope can really be defined as the vertical change divided by the horizontal change. (Rise over Run)
The slope of a line passing through two points (x1, y1), and (x2, y2) can be found using the following formula”
m = =

15. GUIDED PRACTICE
for Examples 1 and 2
Find the slope of the line passing through the given points.
3. (0, 3), (4, 8)
SOLUTION
Let (x1, y1) = (0, 3) and (x2, y2) = (4, 8).
m =
y2 – y1
x2 – x1 =
8 – 3
4 – 0 = 5 4
ANSWER 5 4

16. GUIDED PRACTICE
for Examples 1 and 2
(– 5, 1), (5, – 4)
SOLUTION
Let (x1, y1) = (– 5, 1) and (x2, y2) = (5, – 4)
m =
y2 – y1
x2 – x1 =
– 4 – 1
5 – (–5) = 1 2 –
ANSWER 1 2 –

17. GUIDED PRACTICE
for Examples 1 and 2
(– 3, – 2), (6, -2)
SOLUTION
Let (x1, y1) = (– 3, – 2) and (x2, y2) = (6, -2).
m =
y2 – y1
x2 – x1 =
-2 –( – 2)
6 – (–3) = 9
ANSWER
= 0

18. GUIDED PRACTICE
for Examples 1 and 2
(7, 3), (7, -1)
SOLUTION
Let (x1, y1) = (7, 3) and (x2, y2) = (7, -1).
m =
y2 – y1
x2 – x1 =
-1 – 3
7 – 7 = 4 –
= Undefined
ANSWER

19. Finding Slope on a Graph or Real Object
You can also find the slope of a graphed line or real object by using rise/run
Pick two points on the graph or object and then look at the rise and run between the points
The units must be the same for rise and run

20. y-axis -7 x-axis 13 m = -7/13 1 2 6 3 4 5 7 8 9 10 -2 -6 -3 -4 -5 -7-2 -6 -3 -4 -5 -7 -8 -9 -1 -7 13
m = -7/13

21. y-axis Run 10 Rise 9 x-axis m = 9/10 1 2 6 3 4 5 7 8 9 10 -2 -6 -3 -4-2 -6 -3 -4 -5 -7 -8 -9 -1
Run 10
Rise 9
m = 9/10

22. Slope Intercept Format
Recall from Algebra-1
y = mx + b
m is the slope
b is the y-intercept value

23. Looking at X and Y-Intercept
(0,4)
(3,0)

24. Finding x and y Intercepts
The x-intercept is the x-coordinate of the point it crosses the x-axis.
Likewise, the y-intercept is the y-coordinate of the point crossing the y-axis.
The x-intercept is the value of x when y=0
The y-intercept is the value of y when x=0

25. Example 1 5x – 3y = 15 (Find x & y intercepts) x intercept is when y=0
x = 3 (So the x intercept is (3,0)
y intercept is when x=0
5(0) – 3y = 15
-3y = 15
y = -5 (So the y intercept is (0,-5)

26. Graphing Example 1
(3,0)
(0,-5)

27. Graphing with slope
If we know the slope of a line (m) and at least one ordered pair on the line (x1, y1), then we can graph the line.
First: Plot the known point
Second: Use the slope (rise over run) to find more points
Last: Connect the points with a straight line

28. Graph: m = -4, (3,4) 28

29. Graph line thru Point (-2,-5) with slope of 3/529

30. Graphing with Slope-Intercept
Another method to graph quickly is to get the equation in Slope-Intercept Format
This gives us the slope (m) and Y-Intercept (b)

31. Slope Intercept Form y = mx + b m is the slope of the line
b is the y-intercept point

32. y-axis y=-3x + 2 x-axis 1 2 6 3 4 5 7 8 9 10 -2 -6 -3 -4 -5 -7 -8 -9-2 -6 -3 -4 -5 -7 -8 -9 -1
y=-3x + 2

33. y-axis x-axis y=2/3x - 3 1 2 6 3 4 5 7 8 9 10 -2 -6 -3 -4 -5 -7 -8 -9-2 -6 -3 -4 -5 -7 -8 -9 -1
y=2/3x - 3

34. Constant Linear Lines
What do these look like???

35. Getting Slope-Intercept Format
Many times the equation is not in Slope-Intercept Format y = mx + b
The goal is to get y all by itself on the left side of the equation.
Lets do some examples.

36. 2x + 3y = 9 2x + 3y = 9 (Write equation)
3y = -2x + 9 (Move 2x to the right)
y = -2/3x + 3 (Divide by 3)

37. 3x = 4y + 12 3x = 4y + 12 (Write equation)
4y + 12 = 3x (Flip equation)
4y = 3x (Move 12 to the right)
y = 3/4x – 3 (Divide by 4)

38. Parallel Lines Review
Parallel Lines have the SAME SLOPE
m1 = m2.

39. Perpendicular Lines Review
Perpendicular Lines have NEGATIVE RECIPROCAL SLOPES

40. Finding New Slopes Given y = -3x + 4 What is the parallel slope? -3
What is the perpendicular slope?
1/3

41. Writing an Equation Need slope (m) Need y-intercept (b)
Then just plug in:
y = mx + b

42. Example
Find the slope intercept form of the line with a slope of –2/3 and passes through point (-6,1)
y = mx + b
1 = -2/3(-6) + b
1 = 4 + b
b = -3
y = -2/3x -3

43. Homework
WS 1-3