1. Please read the following and consider yourself in it.
An Affirmation
Please read the following and consider yourself in it.
I am capable of learning. I can accomplish mathematical tasks. I am ultimately responsible for my learning.

2. Standards MGSE9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. (Focus on quadrilaterals, right triangles, and circles.) MGSE9-12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). MGSE9-12.G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. MGSE9-12.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

3. Objectives MGSE9-12.G.GPE.5 SWBAT Prove the slope criteria for parallel and perpendicular lines IOT solve geometric problems. SWBAT Apply slope criteria IOT synthesize the equation of a line parallel or perpendicular to a given line that passes through a given point.

4. What is the slope of the line MN for M(–3, 4) and N(5, –8)?B. C. D.
5-Minute Check 1

5. What is the slope of the line MN for M(–3, 4) and N(5, –8)?B. C. D.
5-Minute Check 1

6. What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?B. C. D.
5-Minute Check 2

7. What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?B. C. D.
5-Minute Check 2

8. What is the graph of the line that has slope 4 and contains the point (1, 2)?
A. B.
C. D.
5-Minute Check 4

9. What is the graph of the line that has slope 4 and contains the point (1, 2)?
A. B.
C. D.
5-Minute Check 4

10. What is the graph of the line that has slope 0 and contains the point (–3, –4)?
A. B.
C. D.
5-Minute Check 5

11. What is the graph of the line that has slope 0 and contains the point (–3, –4)?
A. B.
C. D.
5-Minute Check 5

12. Mathematical Practices 4 Model with mathematics.
Content Standards
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Mathematical Practices
4 Model with mathematics.
8 Look for and express regularity in repeated reasoning.
CCSS

13. slope-intercept form
point-slope form
Vocabulary

14. Concept

15. y = mx + b Slope-intercept form y = 6x + (–3) m = 6, b = –3
Slope and y-intercept
Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line.
y = mx + b Slope-intercept form
y = 6x + (–3) m = 6, b = –3
y = 6x – Simplify.
Example 1

16. Slope and a Point on the Line
Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Then graph the line.
Point-slope form
Simplify.
Example 2

17. Graph the given point (–10, 8).
Slope and a Point on the Line
Answer:
Graph the given point (–10, 8).
Use the slope to find another point 3 units down and 5 units to the right.
Draw a line through these two points.
Example 2

18. Graph the given point (–10, 8).
Slope and a Point on the Line
Answer:
Graph the given point (–10, 8).
Use the slope to find another point 3 units down and 5 units to the right.
Draw a line through these two points.
Example 2

19. Write an equation in point-slope form of the line whose slope is that contains (6, –3).B. C. D.
Example 2

20. Write an equation in point-slope form of the line whose slope is that contains (6, –3).B. C. D.
Example 2

21. Step 1 First, find the slope of the line.
Two Points
A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0).
Step 1 First, find the slope of the line.
Slope formula
x1 = 4, x2 = –2, y1 = 9, y2 = 0
Simplify.
Example 3

22. Distributive Property
Two Points
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (4, 9):
Distributive Property
Add 9 to each side.
Answer:
Example 3

23. Distributive Property
Two Points
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (4, 9):
Distributive Property
Add 9 to each side.
Answer:
Example 3

24. Step 1 First, find the slope of the line.
Two Points
B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3).
Step 1 First, find the slope of the line.
Slope formula
x1 = –3, x2 = –1, y1 = –7, y2 = 3
Simplify.
Example 3

25. Distributive Property
Two Points
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (–1, 3):
m = 5, (x1, y1) = (–1, 3)
Distributive Property
Add 3 to each side.
y = 5x + 8
Answer:
Example 3

26. Distributive Property
Two Points
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (–1, 3):
m = 5, (x1, y1) = (–1, 3)
Distributive Property
Add 3 to each side.
y = 5x + 8
Answer:
Example 3

27. This is a horizontal line.
Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form.
Step 1
Slope formula
This is a horizontal line.
Example 4

28. Subtract 2 from each side. y = –2
Horizontal Line
Step 2
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Simplify.
Subtract 2 from each side.
y = –2
Answer:
Example 4

29. Subtract 2 from each side. y = –2
Horizontal Line
Step 2
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Simplify.
Subtract 2 from each side.
y = –2
Answer:
Example 4

30. Concept

31. y = mx + b Slope-Intercept form 0 = –5(2) + b m = –5, (x, y) = (2, 0)
Write Equations of Parallel or Perpendicular Lines
y = mx + b Slope-Intercept form
0 = –5(2) + b m = –5, (x, y) = (2, 0)
0 = –10 + b Simplify.
10 = b Add 10 to each side.
Answer:
Example 5

32. y = mx + b Slope-Intercept form 0 = –5(2) + b m = –5, (x, y) = (2, 0)
Write Equations of Parallel or Perpendicular Lines
y = mx + b Slope-Intercept form
0 = –5(2) + b m = –5, (x, y) = (2, 0)
0 = –10 + b Simplify.
10 = b Add 10 to each side.
Answer: So, the equation is y = –5x + 10.
Example 5

33. A. y = 3x
B. y = 3x + 8
C. y = –3x + 8 D.
Example 5

34. A. y = 3x
B. y = 3x + 8
C. y = –3x + 8 D.
Example 5

35. A = mr + b Slope-intercept form A = 525r + 750 m = 525, b = 750
Write Linear Equations
RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee.
A. Write an equation to represent the total first year’s cost A for r months of rent.
For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750.
A = mr + b Slope-intercept form
A = 525r m = 525, b = 750
Answer:
Example 6

36. A = mr + b Slope-intercept form A = 525r + 750 m = 525, b = 750
Write Linear Equations
RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee.
A. Write an equation to represent the total first year’s cost A for r months of rent.
For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750.
A = mr + b Slope-intercept form
A = 525r m = 525, b = 750
Answer: The total annual cost can be represented by the equation A = 525r
Example 6

37. Evaluate each equation for r = 12.
Write Linear Equations
RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee.
B. Compare this rental cost to a complex which charges a $200 annual maintenance fee but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?
Evaluate each equation for r = 12.
First complex: Second complex:
A = 525r A = 600r + 200
= 525(12) r = 12 = 600(12) + 200
= 7050 Simplify. = 7400
Example 6

38. Write Linear Equations
Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.
Example 6

39. A. Write an equation to represent the total cost C for d days of use.
RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit.
A. Write an equation to represent the total cost C for d days of use.
A. C = 25 + d + 100
B. C = 125d
C. C = 100d + 25
D. C = 25d + 100
Example 6a

40. A. Write an equation to represent the total cost C for d days of use.
RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit.
A. Write an equation to represent the total cost C for d days of use.
A. C = 25 + d + 100
B. C = 125d
C. C = 100d + 25
D. C = 25d + 100
Example 6a

41. RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit.
B. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate?
A. first company
B. second company
C. neither
D. cannot be determined
Example 6b

42. RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit.
B. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate?
A. first company
B. second company
C. neither
D. cannot be determined
Example 6b