Any questions on the Section 3'3 homework

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Any questions on the Section 3.3 homework?
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Now please CLOSE YOUR LAPTOPS and turn off and
put away your cell phones.
Sample Problems Page Link (Dr. Bruce Johnston)
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Section 3.4 The Slope of a Line

• Slope of a line
• Informally, slope is the tilt of a line.
• It is the ratio of vertical change to horizontal
  change, or

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• Find the slope of the line through (4, -3) and
  (2, 2).
• If we let (x1, y1) be (4, -3) and (x2, y2) be (2,
  2), then

Note If we let (x1, y1) be (2, 2) and (x2, y2)
be (4, -3), then we get the same result.
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• Find 2 points on the graph, then use those points
  in the slope formula.

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Which points do you use? Its your choice, but
its much easier if you pick points whose x- and
y-coordinates are both integers.
(2, 2)
Slope -4 2 -6 3 3 0 2
-2 1
(0, -4)
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• Slope-intercept form of a line
• y mx b
• has a slope of m and has a y-intercept of (0, b).
• This form is useful for graphing, since you have
  a point and the slope readily visible.

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• Find the slope and y-intercept of the line 3x
  y -5.
• First, we need to solve the linear equation for y
• By adding 3x to both sides, y 3x 5.
• Once we have the equation in the
  form of y mx b, we can read the
  slope and y-intercept.
• ? slope is 3
• ? y-intercept is (0,-5)

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• Find the slope and y-intercept of the line 2x
  6y 12.
• First, we need to solve the linear equation for
  y.
• -6y -2x 12 (subtract 2x from both sides)

• Since the equation is now in the form of y mx
  b,
• ? slope is 1/3
• ? y-intercept is (0,-2)

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Example from todays homework
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• For any 2 points, the y values will be equal to
  the same real number.
• The numerator in the slope formula 0 (the
  difference of the y-coordinates), but the
  denominator ? 0 (two different points would have
  two different x-coordinates).
• So the slope 0.

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• For any 2 points, the x values will be equal to
  the same real number.
• The denominator (x2 x1) in the slope formula
  0
• so the slope is undefined (since you cant divide
  by 0).

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Example from todays homework
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Summary of relationship between graphs of lines
and slope

• If a line moves up as it moves from left to
  right, the slope is positive.
• If a line moves down as it moves from left to
  right, the slope is negative.
• Horizontal lines have a slope of 0.
• Vertical lines have undefined slope (or no slope).

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• Two lines that never intersect are called
  parallel lines.
• Parallel lines have the same slope
• unless they are vertical lines, which have no
  defined slope.
• Vertical lines are also parallel to each other,
  even though their slope in undefined.

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• Two lines that intersect at right angles are
  called perpendicular lines.
• Two nonvertical perpendicular lines have slopes
  that are negative reciprocals of each other.
• The product of their slopes will be 1.
• Horizontal and vertical lines are perpendicular
  to each other.

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• Determine whether the following lines are
  parallel, perpendicular, or neither.
• -5x y -6 and x 5y 5
• First, we need to solve both equations for y.
• In the first equation,
• y 5x 6 (add 5x to both sides)
• In the second equation,
• 5y -x 5 (subtract x from both sides)

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• Determine whether the following lines are
  parallel, perpendicular, or neither.
• -x 2y -2 and 2x 4y 3
• In the first equation,
• 2y x 2 (add x to both sides)

• In the second equation,
• 4y 2x 3 (subtract 3 from both
  sides)

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Example from todays homework
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Web site that shows the effect of changing slope
and y-intercept http//www.mathsisfun.com/g
raph/straight_line_graph.html
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A quick way to check if you goofed on a negative
sign Graph the two points and see if the slope
should be positive or negative.
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Watch out for this problem
Hint To start this problem, convert both
distances to the same units.
Also, make sure you type a 0 before decimals lt 1.
(e.g. type 0.08, not just .08.)
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• Note You will be given sheet containing formulas
  to use on quizzes/tests. You can print off a copy
  of the formula sheet to use while you do your
  homework and practice quizzes/tests by clicking
  on the Formula sheet menu button.
• It is a good idea to print a copy of this sheet
  (or keep a yellow copy that weve handed out in
  class) to use while you do your homework
  assignments and practice quizzes/tests so you can
  get used to the location of the formulas and know
  which ones will be available to you on the sheet.
  
• (You will be given a clean copy of the sheet to
  use at each quiz and test, so dont plan to rely
  on any notes you might write on your copy of the
  formula sheet...)

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• Note The homework for this section shouldnt
  take too long, so you might want to look ahead at
  section 3.5 on slope-intercept equations of
  lines. (The homework for that section is a longer
  assignment so you might want to get a head start)

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Reminder

• This homework assignment
• on Section 3.4 is due
• at the start of
• next class period.

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You may now OPEN your LAPTOPS and begin working
on the homework assignment.