• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
3 1 lines
 

3 1 lines

on

  • 924 views

 

Statistics

Views

Total Views
924
Views on SlideShare
924
Embed Views
0

Actions

Likes
0
Downloads
15
Comments
0

0 Embeds 0

No embeds

Accessibility

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    3 1 lines 3 1 lines Presentation Transcript

    • Lines
      • Linear equation – a polynomial equation of the first degree
      • The term “linear” stems from the fact that the graph of such an equation is a straight line.
      • Forms:
      • To graph a line, we generate a pair of points using its equation and then connect the two points.
      • Example. If the linear equation is , a pair of points is generated when we let x = 0 and then x = 1 .
      • Connecting the two points (0,1) and give us the graph of the line.
      • Special cases:
      • y = b
      • x = a
      • The slope of a line describes its incline.
      • The higher the value of the slope, the steeper the incline is.
      • The slope is also defined as a rate of change (the ratio of the change in y coordinate to the change in x coordinate between any two points on the line).
      • If the line is not vertical and ( x 1 , y 1 ) and ( x 2 , y 2 ) are distinct points on the line, then the slope of the line is
      • Example. Find the slope of the line that passes through the points ( - 1,0) and (3,8) .
      • The slope m is given by
      • The slope of a horizontal line is zero while that of a vertical line is not defined.
      • Two non-vertical lines are parallel if and only if m 1 = m 2 .
      • Two lines are perpendicular if and only if m 1 m 2 = - 1 .
      • Example. What is the slope of the line parallel to the line whose equation is ?
      • Rewrite the given equation into the form y = mx + b . The slope is the coefficient m of x .
      • Hence, the slope of the given line is 2.
      • Since two parallel lines have equal slopes, the other line must also have a slope of 2.
      • Linear equations can be rewritten into several different forms. These forms are collectively referred to as “equations of the straight line”.
      • Slope-intercept form: y = mx + b , where m is the slope and b is the y -intercept
      • Illustration. The equation of the line with slope 2 and y -intercept –5 is
      • Two-point form: , with . the line passing through the points ( x 1 , y 1 ) and ( x 2 , y 2 )
      • Illustration. The equation of the line which passes through (2,1) and (-1,5) is
      • Point-slope form: y – y 1 = m ( x – x 1 ) , with the line having a slope m and passing through the point ( x 1 , y 1 )
      • Illustration. The equation of the line whose slope is and passes through (3,5) is
      • Intercept form: , with x -intercept a and . y -intercept b
      • Illustration. The equation of the line with y -intercept 5 and x -intercept - 1 is
      • 1.a Graph the line with slope and passing through the point (1,4) .
      • From (1,4), move 2 units up and then 3 units to the right. Connect the points.
      • 1.b Graph the line with slope and passing through the point (2,5) .
      • From (2,5), move 1 unit up and then 4 units to the left (or 1 unit down and then 4 units to the right)
      • 2.a Find the slope and y - intercept of the line 2 x – y = 4 .
      • 2.d Find the slope and y - intercept of the line 3( y + 1) = 2( x – 5) .
      • 3.a Find an equation of the line passing through (4,3) and (2,5) . Express your answer in slope-intercept form.
      • 3.d Find an equation of the line passing through (3,2) and has slope 3 . Express your answer in slope-intercept form.
      • 3.g Find an equation of the line with slope 4 and y -intercept 2 . Express your answer in slope-intercept form.
      • 4.a Graph .
      • Draw a line through (0,200) and (1,225).
      • 5.a Find an equation of the line passing through ( - 2,4) and is perpendicular to the line 4 x + 3 y = 2 . Express your answer in slope-intercept form.
      • 5.c Find an equation of the line passing through (1,4) and is parallel to the line - 4 x + 6 y = 2 . Express your answer in slope-intercept form.
      • 5.g Find an equation of the line passing through (4, - 3) and has a slope of 0 . Express your answer in slope-intercept form.
      • If the slope is 0, the line is horizontal.
      • So our line is a horizontal line passing through (4, - 3) .
      • The equation is y = –3 .
      • 6.a Are the following pairs of lines parallel, perpendicular, or neither?