Three special types of lines
| 1. Horizontal lines, m = 0 |
2. Vertical lines, m-undefined |
3. Lines through the origin, b = 0 |
1. Horizontal lines, m=0
| Horizontal (y = b)
(For every x-value) |
m = 0 (Zero) |
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Every point on a horizontal line has the same second number, for all x-values.
| Example 1: Find the equation of the line
if m = 0 and b = - 3.
Equation: y = - 3
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Example 2:
Given two points with the same
second number: (2, 5), (- 7, 5)
Equation: y = 5 |
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2. Vertical lines, m-undefined
| 2. Vertical (x = a)
(For every y-value) |
m = (Not Defined) |
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Every point on a vertical line has the same first number, for all y-values.
| Example 1:
Find the equation of the line
if a = 4. m is undefined
Equation: x = 4
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Example 2:
Given two points with the same
first number: (- 7, 5), (- 7, - 3)
Equation: x = - 7 |
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3. Lines through the origin: y = m x → [ b = 0 ]
If a line goes through the origin the y-intercept is (0, 0), and b = 0
 y = m x
| The Line is: |
The Slope is: |
Example |
| Rising as x moves from left to right |
m > 0, (Positive)
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| Falling as x moves from left to right |
m < 0, (Negative) |
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Note1: Since one point is the origin (0, 0), the slope to the other point (x1 , y1) is the ratio m = y1 / x1
Note2: Since one point is the origin (0, 0), if the slope is the ratio
m = y1 / x1 then another point is (x1 , y1).
| Example 1:
Equation: y = 5/2 x, m > 0
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Example 2:
Equation: y = - 2/3 x, m < 0
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| From (0, 0)
the second number is: (2, 5) or (- 2, - 5)
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From (0, 0)
the second number is: (3, - 2) or (- 3, 2) |
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