The document discusses slope and linear equations. It defines slope as the ratio of vertical change to horizontal change between two points on a line. Slope is also known as "rise over run". The document provides examples of finding the slope of lines from graphs and equations. It also gives two examples of using linear equations to model real-world scenarios involving cost as a function of an input variable. Finally, it introduces the slope-intercept form of a linear equation as y = mx + b, where m is the slope and b is the y-intercept.

1. POD 7 Jan
• Create a slope Circle Map
Slope

2. Definitions of Slope
• The tilt, inclination or steepness of a line
• The ratio of vertical change (rise) to
horizontal change (run).
• The change in y (rise) over the change in x
(run)

3. Tilt or Inclination

4. Vertical Change
Horizontal Change
This ratio is also known as
Rise
Run

5. How many points do you need to
draw a line?
• One
• Two
• Three

6. Graph (3,2) and (-1,-1)

7. Draw a line through the points.

8. Now that we have our line lets
find its slope.
Remember we are finding the following ratio:
Vertical or Rise
Horizontal Run

9. Vertical Change
or the Rise
3

10. Horizontal Change
or the Run
4
3

11. Vertical Rise
Horizontal Run
3
4

12. Find the slope of the following
line.

13. The slope is…
1
2

14. Find the slope of the line.

15. The slope is….
-3

16. Find the slope of these lines.

17. The slope is…
• Black line 3
• Red Line 1
• Blue Line -1/2

18. Find the slope of these lines

19. The slope is…
• Orange line 0
• Green Line Undefined

20. Slope Intercept
Real Life Example 1
• Oranges from Florida cost $2 per pound.
Let y represent the total cost and x represent
the number of pounds of oranges. Create a
table, then write a linear equation to find the
total cost.
• Total cost = $2 times the number of pounds
• y = 2x

21. Florida Oranges
• y = 2x
• What is the
cost for 2
pounds?
• 10 pounds?

22. Slope Intercept
Real Life Example 2
• Eileen’s limousine service charges a flat fee
of $5 plus $10 per hour. Let y represent the
total cost and x represent the number of
hours. Write a linear equation to find the
total cost.
• Total cost = $10 times the number of hours
+ flat fee
• y = 10x + 5

23. Eileen’s Limousine Service
• y = 10x + 5
• What is the
cost for 1
hour?
• 4 hours?

24. Intercepts
x-intercept is the
y-intercept is point the line
the point the meets the x-axis
line meets the
y-axis x-intercept = 7
y-intercept = 5

25. Slope-Intercept Form
• Slope-intercept form of an equation assigns
meaning to each variable.
• y = mx +b
• In which m represents slope and b
represents your y-intercept.

26. Slope-intercept
y = mx + b
Slope y-intercept

27. Slope-Intercept Form
• To graph this equation first find and plot
your y-intercept.
• Use your slope to locate a second point.
• Lastly draw a line through your two points.

28. slope-intercept equation
.
.
.
. y-intercept (b) = -2
.