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# Section 1.3

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### Section 1.3

1. 1. 1.3 LINEAR EQUATIONS IN TWO VARIABLES
2. 2. Using Slope  Linear Equation in Two Variable  Also know as slope-intercept form  y=mx+b  m = slope, b = y-intercept  Slope  Number of units the line rises (or falls) vertically for each unit of horizontal change from left to right
3. 3. Slope-Intercept Form of the Equation of a Line  Y=mx+b  Graphing a Linear Equation  Y = 2x + 1 m=2 b=1  Since b equals 1, y-intercept is (0, 1)  Since m = 2, line rises 2 units and moves over to the right one unit 2/1
4. 4. Finding the Slope of a Line  y2 - y1 = the change in y = rise  x2 - x1 = the change in x = run  (x1, y1) and (x2, y2) y2 y1 x2 x1 The Slope of a Line Passing Through Two Points  Slope m of the nonvertical line through ( x1, y1) and (x2, y2) is y 2 y1 x2 x1
5. 5. Writing Linear Equations in Two Variables  Point-slope form  y – y1 = m ( x – x1 )  Ex:  Using the point-slope form with m=3 and (x1 , y1) = (1 , -2)  y – y1 = m ( x – x1)  y–(-2)=3(x–1)  y + 2 = 3x – 3  y = 3x – 5 This is written in slope-intercept form
6. 6. Parallel and Perpendicular Line  1. Two distinct nonvertical lines are parallel if and only if their slopes are equal. That is, m1 = m2  2. Two nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, m1 = -1/ m2
7. 7. Finding Parallel and Perpendicular Lines  Find slope of a line that passes through the point ( 2 , -1 ) and is parallel to line 2x – 3y = 5 or y = 2/3x – 5/3  Find a parallel line  Y – ( -1 ) = 2/3 ( x – 2 )  3(y+10=2(x–2)  3y + 3 = 2x – 4  Y = 2/3x – 7/3
8. 8. Applications  Slope of a line can be interpreted as either a ratio or a rate  If the x-axis and y-axis have the same unit of measure, then the slope has no units and is a ratio  If the x-axis and y-axis have different units of measure, then the slope is a rate or rate of change
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