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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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)

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 Example 2: Given two points with the same second number: (2, 5), (- 7, 5) Equation: y = 5

## 2. Vertical lines, m-undefined

 2. Vertical (x = a) (For every y-value) m = (Not Defined)

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 Example 2: Given two points with the same first number: (- 7, 5), (- 7, - 3) Equation: x = - 7

## 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) Falling as x moves from left to right m < 0, (Negative)

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 Example 2: Equation: y = - 2/3 x, m < 0 From (0, 0) the second number is: (2, 5) or (- 2, - 5) From (0, 0) the second number is: (3, - 2) or (- 3, 2)