1. Slope
Algebra 8th Grade

2. Slope is a
measure of
Steepness.

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

4. If given the graph of a line, find the slope by using
Quick Review
If given the graph
of a line, find the
slope by using
rise over run method

5. run = 5
m= rise
run
m= 4/5
rise = 4

6. Find the slope of the line using the graph! RISE OVER RUN

7. Find the slope of the line using the graph! RISE OVER RUN

8. Slope is sometimes
referred to as the
“rate of change”
between 2 points.

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. Where m represents slope
Finding Slope
m = y2 – y1
x2 – x1
Where m represents slope

12. Find the slope of the line through the points (3,7) and (5, 19). x1 y1
m = 19 – 7
5 – 3
m = 12 2
m = 6

13. (3, 4) and (-6, -2)
m = -2 – 4
-6 – 3
m = -6 -9
m = ⅔

14. UDI!
Find the slope of the line through (-2, 1) and (6,7)

15. Do IT! One more time!
Find the slope of the line through (2,5) and (4,7)

16. AND one more time
What is the slope of the line that contains (-3,-2) and(2,2)

17. What if the
numerator is 0?
You have a slope of zero

18. What if the denominator is 0?
You have an undefined slope

19. Slope Intercept Form
y = mx + b

20. What is a linear function?
A linear function is a function that graphs a line.
Direct variations are only part of the family of linear functions. For example y= x + 1 is a linear function but not a direct variation…why?

21. What is a parent function?
A parent function is the simplest equation of a function.
The function y=x or f(x)= x is the linear parent function…so the value of the variable y is always equals to the value of the variable x
How will the graph look??

22. Linear parent function!!

23. More on linear functions….
A linear function has a slope and a y-intercept
The y-intercept is the y-coordinate of the point where a line crosses/intercepts the y-axis
If you know the slope (m) and the y-intercept (b), you can write the equation of the line.

24. A linear relationship between two variables can be represented by a straight line graph and by the equation:
y = mx + b
The rate of change or slope is m, the coefficient of x, and b represents the
y-intercept (when the point crosses the y-axis)

25. Example 1
Identifying Slope and y-Intercept What are the slope and y-intercept of
y= 8x – 4
Use the slope-intercept form y= mx + b
The slope is 8; the y-intercept is – 4.

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

27. Try It Find the slope and y-intercept of each equation. y= -12x – 3

28. Graphing equations using y=mx + b Graph y = 2x + 4
Step 1 The y-intercept is +4. So plot a point at (0, 4)
Step 2 The slope is +2. Use the slope to plot a second point, 2 units up and 1 unit to the right
Step 3 Draw the line through the two points

29. Graph y = – 3x – 1

31. Graph y = 4x + 2

32. Graph y = x –

33. Identify the slope and y-intercept of the equation then graph
y= x + 2

34. Identify the slope and y-intercept of the equation then graph
y= 2x - 1

35. Identify the slope and y-intercept of the equation then graph
y= x + 3

36. Identify the slope and y-intercept of the equation then graph
y = -5x - 2

37. Identify the slope and y-intercept of the equation then graph
y = -4 + x

38. Identify the slope and y-intercept of the equation then graph

39. Identify the slope and y-intercept of the equation then graph
y = x

40. Identify the slope and y-intercept of the equation then graph
y = x + 6

41. Write an equation of a line y=mx + b with the given slope and y-intercept then graph
m= b= 1

42. Write an equation of a line y=mx + b with the given slope and y-intercept then graph
m= b= -3

43. Write an equation of a line y=mx + b with the given slope and y-intercept then graph
m= b= -1

44. Write an equation of a line y=mx + b with the given slope and y-intercept then graph
m= b= 0

45. Write an equation of a line y=mx + b with the given slope and y-intercept then graph
m= 4 b= 8

46. Slope Intercept Form continued>>>
y = mx + b

47. What if the equation is not in the form y=mx+b??

48. Example y - 2x = -3 Any Ideas???
First, solve the equation for y (isolate the variable y) so it looks as y= mx+b …Apply skills you already know
Example y - 2x = -3
What will you first do to isolate y?

49. UDI
Identify m and b, then graph y + 2x= 6 3

50. Remember *First, solve the equation for y...so it looks as y= mx+b
Find the slope and y-intercept of the following equation 3x + 5y = 10
Remember *First, solve the equation for y...so it looks as y= mx+b
3x + 5y = 10
5y = -3x + 10
y = -3/5 x + 2
m= -3/5
b = 2

51. Remember: First, solve the equation for y...so it looks as y= mx+b
Find the slope and y-intercept of the following equation -6x + 3y = -12. Then graph
Remember: First, solve the equation for y...so it looks as y= mx+b
-6x+3y = -12

52. UDI!
Identify the y-intercept and slope of the line represented by the equation 4x+ y = 3. Then graph

53. UDI
Write 2x – y = 5 as y-intercept form (y= mx + b) then graph

54. Independent Practice

55. Applying Linear Functions
Applying what you know!

56. Applying Linear Functions continued…
Activity of the Day!
Applying Linear Functions continued…
Create a board that models your assigned word problems using:
A linear function (equation)
A table of values with at least six reasonable input values and their corresponding output values. (Input of zero must be included)
A graph that contains appropriate labels for both, the independent and dependent variable.
An interpretation of the slope of the graph and the y-intercept

57. Standard Form PH School PPT and Quick Player Video
Quick Graphs!

58. Point-Slope Form

59. Where m is the slope and b is the intercept
What we Know so far….
Slope Intercept Form
Where m is the slope and b is the intercept
Standard Form

60. The New Stuff… Point- Slope Form
Point- Slope form is:
Where m is the slope and (x1,y1) is the given point

61. Point-Slope Form
y - y₁ = m (x - x ₁)

62. Example
Write the equation of the line that has slope that passes through the point (-1, 7)
Step 1. Use point-slope form y - y₁ = m (x - x₁)
Step 2. Substitute (-1, 7) for x₁ and y₁ , and -3 for m
Step 3. Simplify y -7 = -3 (x + 1)
y-7 = -3x – 3
y= -3x + 4

63. UDI
Write the equation of the line (3, -4); m =6

64. UDI
Write the equation of the line (1, -8); m = -1/5

65. First find the slope m = y2 – y1
Example
Find the equation of the line passing through the given point (2 , 3) and (-1, -5)
First find the slope m = y2 – y1
x2 – x1

66. Example continued...
Then use one of the points to find the point-slope form of the equation y - y₁ = m (x - x₁)
(2 , 3) and (-1, -5)
Finally rewrite point slope as y-intercept form!

67. UDI!
Write and equation for the line in point-slope form, then rewrite the equation in slope-intercept form (6, -4) , (-3, 5)

68. UDI!
Write and equation for the line in point-slope form, then rewrite the equation in slope-intercept form (1, 4) , (-1, 1)

69. UDI!
Write and equation for the line in point-slope form, then rewrite the equation in slope-intercept form (2, 4) , (-3, -6)