Units 8

1
Units 8 9
Slope (all forms) Function Tables Function
Rules Direct Variation Parallel Perpendicular
Lines Scatter Plots Equations of Lines Problem
Solving
2
Slopes, Function Tables, Function Rules

• Slope Its Forms
• Tells how far one point is from another on
  the coordinate plane (graph)
• aka RISE over RUN (You rise or fall then
  run left or right to get from one pt to the
  next.)
• Forms
• 1. Slope-intercept (most common) -
• y mx b where m slope and
• b y-intercept
• 2. Standard Ax By C where A, B, C
  are all numbers

3

• 3. Point-Slope Form - when a point and
• slope are given y y1 m (x x1)
• Function Tables
• Shows the list of xs and ys in relation
  to their function rule (shows inputs outputs)
• C. Function Rules
• An equation that explains the relationship
  between x y. When you plug a value in for x
  (any value), you will get y.

4
Direct Variation

• Formula y kx , where k can NOT 0
• k is the constant of
  variation or
• the in front of x
• y varies directly to x
• B. When is an equation a direct variation?
• - When you solve for y and there is no
  number (other than zero) AFTER the x value.

5

• C. How do you write an equation for direct
  variation?
• 1. When given a point such as (4,-3)
• y kx now plug your points in.
• -3 k(4) solve for k.
• -3/4 k now plug k into the original
• formula
• y -3/4x

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Examples

• Is each equation a direct variation? (y/n)
• 1) 7y 2x 2) 3y 4x 8 3) y -7.5x
  0
• yes no
  yes
• B. Write an equation of the direct variation that
  includes the given point
• 1. (1,5) 2. (-2,3)
  3. (-5,-10)
• y 5x y -3/2x y
  2x

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• C. Real-World Problems Write a direct variation
  to solve.
• The perimeter of a regular octagon varies
  directly with the length of one side of the
  octagon.
• P 8L
• 2. When you have a job that pays an hourly wage,
  the amount you can earn varies directly with the
  number of hours you work. Suppose you earn 7.10
  an hour working at the library.
• E 7.10h

8
Parallel Perpendicular Lines

• Parallel Lines run side by side never cross
  (think gymnastics bars)
• - Slopes are the same
• Perpendicular lines form a 90 degree angle
  (think of an intersection on the highway)
• - Slopes are OPPOSITES in every way if one is
  positive, the other is negative if one is 3, the
  other is 1/3. Therefore, they are NEGATIVE
  RECIPRICOLS of each other.

9
Think about how you write equations for regular
lines

• Find where it crosses the y-axis so that you have
  your b in your formula.
• Find the slope by RISE/RUN from one point to
  another so you have your m for the formula.
• Put it all together in Slope-Intercept form
• y mx b

10
Now ponder this.

• How would you write an equation for a line you
  had not yet seen, BUT you know it contains the
  points (5,1) AND its parallel to y 3/5 x 4??
• What will the slope be?? 3/5
• What will the y-intercept be?? This is where
  slope-intercept comes into play
• y 3/5x b gt 1 3/5(5) b gt1 3 bgt -2b
• Solve for y y 3/5 x 2

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What about a line that passes through (0, -2) and
is perpendicular to y 5x 3??

• What is the slope going to be?? - 1/5
• Plug everything into SLOPE-INTERCEPT form, using
  your y point in place of b
• y mx b
• y -1/5x 2
• To find the y-intercept (-2 in this case), you
  will need to plug the points slope into the
  ymxb formula and solve for b
• -2 -1/5 (0) b gt -2 0 b gt -2 b