3'1 Reading Graphs Linear Equations in Two Variables

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3.1 Reading GraphsLinear Equations in Two
Variables

• A linear equation in two variables can be put in
  the formwhere A, B, and C are real numbers
  andA and B are not zero

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3.1 Reading GraphsLinear Equations in Two
Variables

• Table of values

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3.1 Reading GraphsLinear Equations in Two
Variables

• Points (2, 3)2 is the x-coordinate, 3 is the
  y-coordinate
• Quadrants

I xgt0 and ygt0
II xlt0 and ygt0
III xlt0 and ylt0
IV xgt0 and ylt0
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3.2 Graphing Linear Equations in Two Variables

• The graph of any linear equation in two variables
  is a straight line. Note Two points determine a
  line.
• Graphing a linear equation
• Plot 3 or more points (the third point is used as
  a check of your calculation)
• Connect the points with a straight line.

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3.2 Graphing Linear Equations in Two Variables

• Finding the x-intercept (where the line crosses
  the x-axis) let y0 and solve for x
• Finding the y-intercept (where the line crosses
  the y-axis) let x0 and solve for yNote the
  intercepts may be used to graph the line.

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3.2 Graphing Linear Equations in Two Variables

• If yk, then the graph is a horizontal line
• If xk, then the graph is a vertical line

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3.3 The Slope of a Line

• The slope of a line through points (x1,y1) and
  (x2,y2) is given by the formula
• If the line is horizontal, m 0.
• If the line is vertical, m undefined.

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3.3 The Slope of a Line

• A positive slope rises from left to right.
• A negative slope falls from left to right.
• Finding the slope of a line from its equation
• Solve the equation for y.
• The slope is given by the coefficient of x

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3.3 The Slope of a Line

• Parallel lines (lines that do not intersect) have
  the same slope.
• Perpendicular lines (lines that intersect to form
  a 90? angle) have slopes that are negative
  reciprocals of each other.
• Horizontal lines and vertical lines are
  perpendicular to each other

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3.4 Equations of Lines

• General form Ax By C
• Slope-intercept form y mx b(where m
  slope and b y-intercept)
• Point-slope form The line with slope m going
  through point (x1, y1) has the equation y y1
  m(x x1)

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3.4 Equations of Lines

• Example Find the equation in slope-intercept
  form of a line passing through the point (-4,5)
  and perpendicular to the line 2x 3y 6(solve
  for y to get slope of line)(take the negative
  reciprocal to get the ? slope)

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3.4 Equations of Lines

• Example (continued)Use the point-slope form
  with this slope and the point (-4,5) In slope
  intercept form