Post on 16-Jul-2020
Here is a line.
Here is a line.
• ••
•
•
•
We mark the points on the line
with coordinates
that are integers.
Here is a line.
• ••
•
•
•
To get from the bottom point to the next marked point is 2 up and 3 right.
2 up3 right
Here is a line.
• ••
•
•
•
The coordinates of the two points are:
(-6, -9)and
(-3, -7) 2 up3 right
Here is a line.
• ••
•
•
•
The coordinates of the two points are:
(-6, -9)and
(-3, -7)
-7 – -9 = -7 + 9 = 2
2 up3 right
• ••
•
•
•
The coordinates of the two points are:
(-6, -9)and
(-3, -7)
-7 – -9 = -7 + 9 = 2
-3 – -6 = -3 + 6 = 3
2 up3 right
Slope =
• ••
•
•
•
The coordinates of the two points are:
(-6, -9)and
(-3, -7)
-7 – -9 = -7 + 9 = 2
-3 – -6 = -3 + 6 = 3
2 up3 right
32
• ••
• •
•
The coordinates of the two points are:
(-3, -7)and
(6, -1)
6 up
9 right
• ••
• •
•
The coordinates of the two points are:
(-3, -7)and
(6, -1)-1 – -7 = -1 + 7
= 6 6 up
9 right
• ••
• •
•
The coordinates of the two points are:
(-3, -7)and
(6, -1)-1 – -7 = -1 + 7
= 66 – -3 = 6 + 3 =
9
6 up
9 right
• ••
• •
•
The coordinates of the two points are:
(-3, -7)and
(6, -1)-1 – -7 = -1 + 7
= 66 – -3 = 6 + 3 =
9
6 up
9 right
Slope = = 32
96
• ••
• •
•10 down
15 left
The coordinates of the two points are:
(-6, -9)and
(9, 1)
• ••
• •
•10 down
15 left
The coordinates of the two points are:
(-6, -9)and
(9, 1)
1 – -9 = 1 + 9 = 10
• ••
• •
•10 down
15 left
The coordinates of the two points are:
(-6, -9)and
(9, 1)
1 – -9 = 1 + 9 = 10
9 – -6 = 9 + 6 = 15
• ••
• •
•10 down
15 left
The coordinates of the two points are:
(-6, -9)and
(9, 1)
1 – -9 = 1 + 9 = 10
9 – -6 = 9 + 6 = 15
Slope = = 32
1510
Here is another line.
• ••• •
• ••• •4 down
16 right
The coordinates of the two points are:
(-9, 6)and
(7, 2)
• ••• •4 down
16 right
The coordinates of the two points are:
(-9, 6)and
(7, 2)
2 – 6 = 2 + -6 = -4
• ••• •4 down
16 right
The coordinates of the two points are:
(-9, 6)and
(7, 2)
2 – 6 = 2 + -6 = -4
7 – -9 = 7 + 9 = 16
• ••• •4 down
16 right
The coordinates of the two points are:
(-9, 6)and
(7, 2)
2 – 6 = 2 + -6 = -4
7 – -9 = 7 + 9 = 16
Slope = = 41-16
-4
• ••• • 2 up8 left
The coordinates of the two points are:
(-5, 5)and
(3, 3)
• ••• • 2 up8 left
The coordinates of the two points are:
(-5, 5)and
(3, 3)
3 – 5 = 3 + -5 = -2
• ••• • 2 up8 left
The coordinates of the two points are:
(-5, 5)and
(3, 3)
3 – 5 = 3 + -5 = -2
3 – -5 = 3 + 5 = 8
• ••• • 2 up8 left
The coordinates of the two points are:
(-5, 5)and
(3, 3)
3 – 5 = 3 + -5 = -2
3 – -5 = 3 + 5 = 8
Slope = = 8-2
41-
The slope formula:
Given coordinates, (x1, y1) and (x2, y2), of two points on a line, the
slope, m, of the line is:
y2 – y1
x2 – x1m =
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
8 – 4-1 – 5
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
8 – 4-1 – 5 = 8 + -4
-1 + -5
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
8 – 4-1 – 5 = 8 + -4
-1 + -5= 4
-6
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
8 – 4-1 – 5 = 8 + -4
-1 + -5= 4
-6 = - 2 3
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1x2 y2
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1x2 y2
4 – 85 – -1
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1x2 y2
4 – 85 – -1 = 4 + -8
5 + 1
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1x2 y2
4 – 85 – -1 = 4 + -8
5 + 1 = -46
(5, 4) and (-1, 8)
y2 – y1
x2 – x1m =
x1 y1x2 y2
4 – 85 – -1 = 4 + -8
5 + 1 = -46 = - 2
3
(12, -5) and (0, 15)
y2 – y1
x2 – x1m =
(12, -5) and (0, 15)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
(12, -5) and (0, 15)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
15 – -50 – 12
(12, -5) and (0, 15)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
15 – -50 – 12 = 15 + 5
0 + -12
(12, -5) and (0, 15)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
15 – -50 – 12 = 15 + 5
0 + -12= 20
-12
(12, -5) and (0, 15)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
15 – -50 – 12 = 15 + 5
0 + -12= 20
-12= - 5 3
(12, -5) and (0, -5)
y2 – y1
x2 – x1m =
(12, -5) and (0, -5)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
(12, -5) and (0, -5)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-5 – -50 – 12
(12, -5) and (0, -5)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-5 – -50 – 12 = -5 + 5
0 + -12
(12, -5) and (0, -5)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-5 – -50 – 12 = -5 + 5
0 + -12= 0
-12
(12, -5) and (0, -5)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-5 – -50 – 12 = -5 + 5
0 + -12= 0
-12 = 0
(12, -5) and (0, -5)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-5 – -50 – 12 = -5 + 5
0 + -12= 0
-12 = 0Horizontal line
(7, 0) and (7, -4)
y2 – y1
x2 – x1m =
(7, 0) and (7, -4)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
(7, 0) and (7, -4)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-4 – 07 – 7
(7, 0) and (7, -4)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-4 – 07 – 7 = -4 + 0
7 + -7
(7, 0) and (7, -4)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-4 – 07 – 7 = -4 + 0
7 + -7= -4
0
(7, 0) and (7, -4)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-4 – 07 – 7 = -4 + 0
7 + -7= -4
0 = noslope
(7, 0) and (7, -4)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-4 – 07 – 7 = -4 + 0
7 + -7= -4
0
Vertical line
= noslope
(3.14, -1.6) and (0.46, -1.8)
y2 – y1
x2 – x1m =
(3.14, -1.6) and (0.46, -1.8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
(3.14, -1.6) and (0.46, -1.8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-1.8 – -1.60.46 – 3.14
(3.14, -1.6) and (0.46, -1.8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-1.8 – -1.60.46 – 3.14 = -1.8 + 1.6
0.46 + -3.14
(3.14, -1.6) and (0.46, -1.8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-1.8 – -1.60.46 – 3.14 = = -2.68
-1.8 + 1.6 -0.20.46 + -3.14
(3.14, -1.6) and (0.46, -1.8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-1.8 – -1.60.46 – 3.14 = = -2.68 =
-1.8 + 1.6 -0.20.46 + -3.14
20 268
(3.14, -1.6) and (0.46, -1.8)
y2 – y1
x2 – x1m =
x1 y1 x2 y2
-1.8 – -1.60.46 – 3.14 = = -2.68 =
-1.8 + 1.6 -0.20.46 + -3.14
20 268
= 5
67
The slope formula:
Given coordinates, (x1, y1) and (x2, y2), of two points on a line, the
slope, m, of the line is:
y2 – y1
x2 – x1m =