Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
AA Section 3-5
1. Section 3-5
Finding the Equation of a Line
...or th e Po in t-S lo pe Th eo re m se ct io n
2. Warm-up
Write an equation for the line through the pair of points
a. (5, 9), (5, -2) b. (9, 1), (6, 4)
3. Warm-up
Write an equation for the line through the pair of points
a. (5, 9), (5, -2) b. (9, 1), (6, 4)
x=5
4. Warm-up
Write an equation for the line through the pair of points
a. (5, 9), (5, -2) b. (9, 1), (6, 4)
x=5 y = -x + 10
5. Warm-up
Write an equation for the line through the pair of points
a. (5, 9), (5, -2) b. (9, 1), (6, 4)
x=5 y = -x + 10
Not quite sure how this is done? We’ll see two ways today
8. Question
What determines a line?
Two points
...and once we have two points, we can find an equation
9. Example 1
The formula relating blood pressure and age is linear.
Normal systolic blood pressures are 110 for a 20 year old
and 130 for a 60 year old. Graph the line and find an
equation where blood pressure B is a function of age A.
10. Example 1
The formula relating blood pressure and age is linear.
Normal systolic blood pressures are 110 for a 20 year old
and 130 for a 60 year old. Graph the line and find an
equation where blood pressure B is a function of age A.
130.0
Blood Pressure
97.5
65.0
32.5
0
0 15 30 45 60
Age
18. Example 1 (con’t)
(20, 110), (60, 130)
130 − 110 20 1
m= = =
60 − 20 40 2
B= 2 A+b
1
110 = (20) + b
1
2
110 = 10 + b
b = 100
19. Example 1 (con’t)
(20, 110), (60, 130)
130 − 110 20 1
m= = =
60 − 20 40 2
B= 2 A+b
1
110 = (20) + b
1
2
110 = 10 + b
b = 100
B = 2 A + 100
1
20. Example 1 (con’t)
(20, 110), (60, 130)
130 − 110 20 1
m= = =
60 − 20 40 2
B= 2 A+b
1
110 = (20) + b
1
2
110 = 10 + b
b = 100
B = 2 A + 100
1
There has to be a better way!
22. Point-Slope Theorem
If a line contains (x1, y1) and has slope m, then it has
the equation y - y1 = m(x - x1)
23. Point-Slope Theorem
If a line contains (x1, y1) and has slope m, then it has
the equation y - y1 = m(x - x1)
(In other words, you need a point and the slope)
24. Example 2
Find an equation for the line through (-3, 6) and (5, 0)
using the point-slope theorem.
25. Example 2
Find an equation for the line through (-3, 6) and (5, 0)
using the point-slope theorem.
6−0
m=
−3 − 5
26. Example 2
Find an equation for the line through (-3, 6) and (5, 0)
using the point-slope theorem.
6−0 6
m= =
−3 − 5 −8
27. Example 2
Find an equation for the line through (-3, 6) and (5, 0)
using the point-slope theorem.
6−0 6 3
m= = =−
−3 − 5 −8 4
28. Example 2
Find an equation for the line through (-3, 6) and (5, 0)
using the point-slope theorem.
6−0 6 3
m= = =−
−3 − 5 −8 4
y − y1 = m(x − x1 )
29. Example 2
Find an equation for the line through (-3, 6) and (5, 0)
using the point-slope theorem.
6−0 6 3
m= = =−
−3 − 5 −8 4
y − y1 = m(x − x1 )
3
y − 0 = − 4 (x − 5)
30. Example 2
Find an equation for the line through (-3, 6) and (5, 0)
using the point-slope theorem.
6−0 6 3
m= = =−
−3 − 5 −8 4
y − y1 = m(x − x1 )
3
y − 0 = − 4 (x − 5)
3 15
y=−4x+ 4
31. When dealing with real world situations,
deal with the problem as we always
have: find the equation first, then
answer the question.
32. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
33. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
34. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” =
35. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 =
36. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
37. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
5’1” =
38. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
5’1” = 5(12) + 1 =
39. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
5’1” = 5(12) + 1 = 61”
40. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
5’1” = 5(12) + 1 = 61”
6’ = 6(12) = 72”
41. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
5’1” = 5(12) + 1 = 61”
6’ = 6(12) = 72”
(58”, 109 lbs)
42. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
5’1” = 5(12) + 1 = 61”
6’ = 6(12) = 72”
(58”, 109 lbs) (61”, 115 lbs)
43. Example 3
The lightest recommended weight for a Martian with
height 4’10” is 109 lbs. This weight increases 2 lbs/in
to a height of 5’1” and then goes up 3 lbs/in to a height
of 6’ which is tall for a Martian.
a. Graph the situation
First, we need to convert all heights to inches
4’10” = 4(12) +10 = 58”
5’1” = 5(12) + 1 = 61”
6’ = 6(12) = 72”
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
44. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
45. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
46. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1)
47. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1)
w - 109 = 2(h - 58)
48. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1)
w - 109 = 2(h - 58)
w = 2h - 7
49. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1)
w - 109 = 2(h - 58)
w = 2h - 7
for 58 ≤ h ≤ 61
50. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1) w - w1 = m(h - h1)
w - 109 = 2(h - 58)
w = 2h - 7
for 58 ≤ h ≤ 61
51. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1) w - w1 = m(h - h1)
w - 109 = 2(h - 58) w - 115 = 3(h - 61)
w = 2h - 7
for 58 ≤ h ≤ 61
52. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1) w - w1 = m(h - h1)
w - 109 = 2(h - 58) w - 115 = 3(h - 61)
w = 2h - 7 w = 3h - 68
for 58 ≤ h ≤ 61
53. Example 3 (con’t)
(58”, 109 lbs) (61”, 115 lbs) (72”, 148 lbs)
b. Find two equations that describe these situations
y - y1 = m(x - x1)
w - w1 = m(h - h1) w - w1 = m(h - h1)
w - 109 = 2(h - 58) w - 115 = 3(h - 61)
w = 2h - 7 w = 3h - 68
for 58 ≤ h ≤ 61 for 61 < h ≤ 72
55. Homework
p. 165 #1 - 21
“ I’m not sure I want popular opinion on my side -- I’ve
noticed those with the most opinions often have the
fewest facts.” - Bethania McKenstry
