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Linear Equations in Two Variables

VIEWS: 3 PAGES: 40

									Linear Equations in Two Variables



   Objective: Write a linear equation in
   two variables given different types of
               information.
 6  12  18
              3
 5  1   6

    m  5; b  7
  y  1x  0
  y  x
Example 1
Example 1
Example 1
Example 1
                      Try This
• Write an equation in slope-intercept form for the line
  containing the points (2, 4) and (1, 6)
                      Try This
• Write an equation in slope-intercept form for the line
  containing the points (2, 4) and (1, 6)

                         64 2
1) Find the slope                 2
                         1  2 1
                      Try This
• Write an equation in slope-intercept form for the line
  containing the points (2, 4) and (1, 6)

                          64 2
1) Find the slope                  2
                          1  2 1

2) Find the y-intercept   y  mx  b
                          4  (2)( 2)  b
                          8b
                       Try This
• Write an equation in slope-intercept form for the line
  containing the points (2, 4) and (1, 6)

                          64 2
1) Find the slope                  2
                          1  2 1

2) Find the y-intercept   y  mx  b
                          4  (2)( 2)  b
                          8b

3) Write an equation      y  mx  b
                          y  2 x  8
              Point-Slope Form
• You can use the point-slope form to write an equation
  of a line if you are given the slope and the
  coordinates of any point on the line or given two
  points.
              Point-Slope Form
• You can use the point-slope form to write an equation
  of a line if you are given the slope and the
  coordinates of any point on the line or given two
  points.
                      Try This
• Write an equation in slope-intercept form for the line
  containing the points (2, 4) and (1, 6)

                         64 2
1) Find the slope                 2
                         1  2 1
                      Try This
• Write an equation in slope-intercept form for the line
  containing the points (2, 4) and (1, 6)

                          64 2
1) Find the slope                  2
                          1  2 1

2) Use point-slope form
                          y  y1  m( x  x1 )
                          y  4  2( x  2)
                          y  4  2 x  4
                          y  2 x  8
                      Try This
• Write an equation in slope-intercept form for the line
  containing the points (2, 4) and (1, 6)

                          64 2
1) Find the slope                  2
                          1  2 1

2) Use point-slope form
                          y  y1  m( x  x1 )   y  y1  m( x  x1 )
                          y  4  2( x  2)     y  6  2( x  1)
                          y  4  2 x  4       y  6  2 x  2
                          y  2 x  8           y  2 x  8
Example 2
Example 2
Example 2
                      Try This
• Write an equation in slope-intercept form for the line
  that has the slope of 3 and contains the point (2, -1).
                      Try This
• Write an equation in slope-intercept form for the line
  that has the slope of 3 and contains the point (2, -1).
• Begin with point-slope form y  y1  m( x  x1 )
                                 y  (1)  3( x  2)
                      Try This
• Write an equation in slope-intercept form for the line
  that has the slope of 3 and contains the point (2, -1).
• Begin with point-slope form y  y1  m( x  x1 )
                                 y  (1)  3( x  2)

• Write an equation              y  1  3x  6
                                 y  3x  7
                  Parallel Lines
• If two lines have the same slope, they are parallel.

• If two lines are parallel, they have the same slope.

• All vertical lines have an undefined slope and are
  parallel to one another.

• All horizontal lines have a slope of 0 and are parallel
  to one another.
Parallel Lines
Example 4
Example 4
        Example 4




y  mx  b
3  (2)(1)  b
1 b
y  2 x  1
        Example 4




y  mx  b
3  (2)(1)  b
1 b
y  2 x  1
             Perpendicular Lines
• If a nonvertical line is perpendicular to another line,
  the slopes of the lines are negative reciprocals of one
  another.

• All vertical lines are perpendicular to all horizontal
  lines.

• All horizontal lines are perpendicular to all vertical
  lines.
Perpendicular Lines
Example 5
Example 5
Example 5



     y  mx  b
      3  (  1 )(4)  b
               4

     2b
     y  1 x2
          4
Example 5
                   Example 3
• Tim leaves his house and drives at a constant speed
  to go camping. On his way to the campgrounds, he
  stops to buy gas. Three hours after buying gas, Tim
  has traveled 220 miles from home, and 5 hours after
  buying gas he has traveled 350 miles from home.
  How far from home was Tim when he bought gas?
                    Example 3
• Write a linear equation to model Tim’s distance, y, in
  terms of time, x. Three hours after buying gas, Tim
  has traveled 220 miles, and 5 hours after buying gas,
  Tim has traveled 350 miles. The line contains the
  points (3, 220) and (5, 350).
                    Example 3
• Write a linear equation to model Tim’s distance, y, in
  terms of time, x. Three hours after buying gas, Tim
  has traveled 220 miles, and 5 hours after buying gas,
  Tim has traveled 350 miles. The line contains the
  points (3, 220) and (5, 350).
                   Example 3
• This equation models Tim’s distance from home with
  respect to time. Since x represents the number of
  hours he traveled after he bought gas, he bought gas
  when x = 0. Thus, he bought gas 25 miles from
  home.
                   Homework
• Pages 26-27
• 11-45 odd

• Please check your answers as you go and do all of the
  problems. You need practice to master this skill!

								
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