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Actmath lnes
1.
LINES
2.
What is the
formula for the distance of a line?
3.
What is the
formula for the distance of a line? D = (𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
4.
What is the
formula for the distance of a line? D = (𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
5.
What is the
formula for the distance of a line? D = (𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
6.
What is the
formula for the distance of a line? D = (𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
7.
What is the
formula for the distance of a line? D = (𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
8.
Let’s ask that
again:
9.
Let’s ask that
again: What is the formula for the distance of a line?
10.
Let’s ask that
again: What is the formula for the distance of a line? Say it out loud.
11.
D = (𝑦2
− 𝑦1)2+(𝑥2 − 𝑥1)2
12.
One more time:
13.
One more time: What
is the formula for the distance of a line?
14.
D = (𝑦2
− 𝑦1)2+(𝑥2 − 𝑥1)2
15.
What is the
distance between point A and Point B? (8,2) (4,-1)
16.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
17.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (𝑦2 − 𝑦1)2+(𝑥2 − 𝑥1)2
18.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (𝟒 − 𝑦1)2+(𝑥2 − 𝑥1)2
19.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (𝟒 − 𝑦1)2+(𝑥2 − 𝑥1)2
20.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (𝟒 − 𝑦1)2+(𝑥2 − 𝑥1)2
21.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (−𝟏 − 𝟐)2+(𝑥2 − 𝑥1)2
22.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (−1 − 2)2+(𝟒 − 𝑥1)2
23.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (−1 − 2)2+(4 − 𝟖)2
24.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (−1 − 2)2+(4 − 8)2
25.
What is the
distance between point A and Point B? (8,2) (4,-1) D = (−𝟑)2+(4 − 8)2
26.
What is the
distance between point A and Point B? (8,2) (4,-1) D = 𝟗 + (4 − 8)2
27.
What is the
distance between point A and Point B? (8,2) (4,-1) D = 9 + (−𝟒)2
28.
What is the
distance between point A and Point B? (8,2) (4,-1) D = 9 + 𝟏𝟔
29.
What is the
distance between point A and Point B? (8,2) (4,-1) D = 𝟐𝟓
30.
What is the
distance between point A and Point B? (8,2) (4,-1) D = 𝟓
31.
What is the
distance between point A and Point B? (8,2) (4,-1) D = 𝟓 The distance between Point A and Point B is 5 units
32.
Last time: What is
the formula for the distance of a line?
33.
D = (𝑦2
− 𝑦1)2+(𝑥2 − 𝑥1)2
34.
What is the
formula for the midpoint of a line?
35.
𝑋1+𝑋2 2 , 𝑌1+𝑌2 2
36.
See if you
can say it before going to the next slide.
37.
Did you get
it right? 𝑋1+𝑋2 2 , 𝑌1+𝑌2 2
38.
What is midpoint
between these two points? (8,2) (4,-1)
39.
What is midpoint
between these two points? (8,2) (4,-1) 𝑋1+𝑋2 2 , 𝑌1+𝑌2 2
40.
What is midpoint
between these two points? (8,2) (4,-1) 𝑋1+𝑋2 2 , 𝑌1+𝑌2 2
41.
What is midpoint
between these two points? (8,2) (4,-1) 𝑋1+𝑋2 2 , 𝑌1+𝑌2 2
42.
What is midpoint
between these two points? (8,2) (4,-1) 𝑋1+𝑋2 2 , 𝑌1+𝑌2 2
43.
What is midpoint
between these two points? (8,2) (4,-1) 𝟒 +𝑋2 2 , 𝑌1+𝑌2 2
44.
What is midpoint
between these two points? (8,2) (4,-1) 𝟒 +𝑋2 2 , 𝑌1+𝑌2 2
45.
What is midpoint
between these two points? (8,2) (4,-1) 𝟒 +𝟖 2 , 𝑌1+𝑌2 2
46.
What is midpoint
between these two points? (8,2) (4,-1) 𝟒 +𝟖 2 , 𝑌1+𝑌2 2
47.
What is midpoint
between these two points? (8,2) (4,-1) 𝟒 +𝟖 2 , −𝟏+𝑌2 2
48.
What is midpoint
between these two points? (8,2) (4,-1) 𝟒 +𝟖 2 , −𝟏+𝑌2 2
49.
What is midpoint
between these two points? (8,2) (4,-1) 𝟒 +𝟖 2 , −𝟏+𝟐 2
50.
What is midpoint
between these two points? (8,2) (4,-1) 𝟏𝟐 2 , −𝟏+𝟐 2
51.
What is midpoint
between these two points? (8,2) (4,-1) 𝟏𝟐 2 , 𝟏 2
52.
What is midpoint
between these two points? (8,2) (4,-1) 6 , 1 2
53.
What is midpoint
between these two points? (8,2) (4,-1) 6 , 1 2
54.
What is midpoint
between these two points? (8,2) (4,-1) 6 , 0.5
55.
What is midpoint
between these two points? (8,2) (4,-1) (𝟔,0.5) The Midpoin t
56.
What is the
formula for a line?
57.
What is the
formula for a line? 𝑦 = 𝑚𝑥 + 𝑏
58.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝑏 This is the slope which usually is a fraction
59.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝒃 This is where the line crosses the Y Axix
60.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝟏 If the y intercept is 1 then the line goes through the Y axis at 1.
61.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝟏 If the y intercept is 1 then the line goes through the Y axis at 1. 1
62.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝟐 If the y intercept is 2 then the line goes through the Y axis at 2 2
63.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝟑 If the y intercept is 3 then the line goes through the Y axis at 3 3
64.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝟒 If the y intercept is 4 then the line goes through the Y axis at 4 4
65.
What is the
formula for a line? 𝑦 = 𝒎𝑥 + 𝟎 If the y intercept is 0 then the line goes through the Y axis at 0 0
66.
Let’s go back
to this formula
67.
Let’s go back
to this formula 𝑦 = 𝒎𝑥 + 𝟏 1 The slope is always a fraction.
68.
Let’s go back
to this formula 𝑦 = 𝒎𝑥 + 𝟏 1 Let’s say the slope is 1/2
69.
Let’s go back
to this formula 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1 Let’s say the slope is 1/2
70.
Let’s go back
to this formula 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1
71.
Let’s go back
to this formula 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1 This is the rise
72.
Let’s go back
to this formula 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1 This is the rise Over the run
73.
Let’s go back
to this formula 𝑦 = 𝟏 2 𝑥 + 1 1 rise1
74.
Let’s go back
to this formula 𝑦 = 1 𝟐 𝑥 + 1 1 run 1 2
75.
1 Let’s go back
to this formula 𝑦 = 1 𝟐 𝑥 + 1 run 1 2
76.
1 Let’s go back
to this formula 𝑦 = 𝟏 𝟐 𝑥 + 1 1 2 1 2
77.
Let’s go back
to this formula 𝑦 = 𝟏 𝟐 𝑥 + 1
78.
Let’s go back
to this formula 𝑦 = 1 2 𝑥 + 𝟏 If the y intercept goes to 0 watch what happens
79.
Let’s go back
to this formula 𝑦 = 1 2 𝑥 + 𝟎 If the y intercept goes to 0 watch what happens
80.
Let’s go back
to this formula 𝑦 = 1 2 𝑥 + 𝟎 If the y intercept goes to 0 watch what happens 0
81.
Let’s go back
to this formula 𝑦 = 1 2 𝑥 + 𝟎 If the y intercept goes to 2 watch what happens 0
82.
Let’s go back
to this formula 𝑦 = 1 2 𝑥 + 𝟐 If the y intercept goes to 2 watch what happens 0
83.
Let’s go back
to this formula 𝑦 = 1 2 𝑥 + 𝟐 If the y intercept goes to 2 watch what happens 2
84.
Without going to
the next slide can you say what the formula for a line is?
85.
Without going to
the next slide can you say what the formula for a line is? 𝒚 = 𝒎𝒙 + 𝒃 Did you get it right?
86.
What does the
“m” mean? 𝒚 = 𝒎𝒙 + 𝒃
87.
slope 𝒚 = 𝟏 𝟐 𝒙 +
𝒃
88.
slope 𝒚 = 𝟏 𝟐 𝒙 +
𝒃 1 1 2
89.
slope 𝒚 = 𝟏 𝟐 𝒙 +
𝒃 1 1 2 rise 1
90.
slope 𝒚 = 𝟏 𝟐 𝒙 +
𝒃 1 1 2 run 2
91.
slope 𝒚 = 𝟏 𝟐 𝒙 +
𝒃 1
92.
What does the
“b” mean? 𝒚 = 𝑚𝒙 + 𝒃
93.
Y - intercept 𝒚
= 𝑚𝒙 + 𝒃 1 1 2 1 2
94.
Y - intercept 𝒚
= 𝑚𝒙 + 𝟏 1 1 2 1 2
95.
Where the line
crosses the Y axis 𝒚 = 𝑚𝒙 + 𝟏 1 1 2 1 2
96.
Where the line
crosses the Y axis 𝒚 = 𝑚𝒙 + 𝟏 1 2 1 2 1
97.
What do parallel
lines have in common?
98.
Let’s go back
to this formula 0 𝑦 = 𝟏 𝟐 𝑥 + 𝟎
99.
Let’s go back
to this formula 0 𝑦 = 𝟏 𝟐 𝑥 + 𝟎
100.
Let’s go back
to this formula 0 𝑦 = 𝟏 𝟐 𝑥 + 𝟎 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1
101.
Let’s go back
to this formula 0 𝑦 = 𝟏 𝟐 𝑥 + 𝟎 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1
102.
0 𝑦 = 𝟏 𝟐 𝑥 +
𝟎 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1 𝑦 = 𝟏 𝟐 𝑥 + 𝟐 2
103.
All these slopes
are the same because the lines are parallel 0 𝑦 = 𝟏 𝟐 𝑥 + 𝟎 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1 𝑦 = 𝟏 𝟐 𝑥 + 𝟐 2
104.
All these slopes
are the same because the lines are parallel 0 𝑦 = 𝟏 𝟐 𝑥 + 𝟎 𝑦 = 𝟏 𝟐 𝑥 + 𝟏 1 𝑦 = 𝟏 𝟐 𝑥 + 𝟐 2
105.
What is the
slope of a perpendicular line to the line below? 𝑦 = 𝟏 𝟐 𝑥 + 𝟐
106.
What is the
slope of a perpendicular line to the line below? 𝑦 = 𝟐 𝟏 𝑥 + 𝟐 Just flip the slope and then multiply by -1
107.
What is the
slope of a perpendicular line to the line below? 𝑦 = 𝟐 𝟏 𝑥 + 𝟐 Just flip the slope and then multiply by -1
108.
What is the
slope of a perpendicular line to the line below? 𝑦 = − 𝟐 𝟏 𝑥 + 𝟐 Just flip the slope and then multiply by -1
109.
What is the
slope of a perpendicular line to the line below? 𝑦 = 𝟑 𝟒 𝑥 + 𝟐
110.
What is the
slope of a perpendicular line to the line below? − 𝟒 𝟑 𝑥
111.
What is the
slope of a perpendicular line to the line below? 𝑦 = 𝟐𝑥 + 𝟐
112.
What is the
slope of a perpendicular line to the line below? − 𝟏 𝟐 𝑥
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