April 03, 2015
Bell Work!
v
Write an equation of the line.
1. passes through (3, 0) and (-5, 2)
2. passes through (0, 9) and is
perpendicular to
y = (-2/3)x - 1
3. m=4, passes through (1, -8)
April 03, 2015
Section 8.P ~ Model Direct Variation
EQ: How do I write a direct variation equation?
What does the graph of a direct variation equation look like?
Direct Variation: is a relationship between x and y
Looks like:
Key Phrase: y varies directly with x
Constant of Variation: the nonzero constant a
Graph: has a slope of a and a y-intercept of 0
Example:
April 03, 2015
Write and graph a direct variation equation
Write and graph a direct variation equation
that has (-4, 8) as a solution.
Plug in x and y
Solve for a
Substitute a
back in
Left Side - YOU TRY!!
Write and graph a direct variation equation
that has the given ordered pair as a
solution.
(3, -9)
April 03, 2015
Write and apply a model for direct variation
a. Write a direct variation equation that has the given
ordered pair as a solution. (–7, 4)
b. Then solve for y when x=2.
Left Side - YOU TRY!!
The variables x and y vary directly. a) Write an equation
that relates x and y. b) Then find y when x = 12.
x = 4, y = 8
April 03, 2015
Identifying Direct Variation
Tell whether the equation below represents direct
variation.
Yes
No
Yes
No
Yes
No
April 03, 2015
Write & apply a model for direct variation (p. 108)
METEOROLOGY
Hailstones form when strong
updrafts support ice particles
high in clouds, where water
droplets freeze onto the
particles.The diagram shows a
hailstone at two different times
during its formation.
a.) write an equation
b.) find the diameter at t=20
April 03, 2015
Use ratios to identify direct variation
Ratios and Direct Variation:
Solve y = ax for a
If the ratio of y to x is constant,
then we have direct variation!
SHARKS
Great white sharks have triangular teeth. The table
below gives the length of a side of a tooth and the
body length for each of six great white sharks. Tell
whether tooth length and body length show direct
variation. If so, write an equation that relates the
quantities.
Tooth length, t (cm) 1.8
Body length, b (cm)
2.4 2.9 3.6 4.7 5.8
215 290 350 430 565 695
Left Side - YOU TRY!!
Determine whether the table shows direct variation.
X 1
2
y
9 11 13 15
7
3
4
5
April 03, 2015
Your weight M on Mars varies directly with your weight E on Earth.
If you weight 116 pounds on Earth, you would weight 44 pounds
on Mars. Which equation relates E and M?
A. M = E - 72
B. 44M = 116E
C. M = (29/11)E
D. M = (11/29)E
April 03, 2015
pg 109
3 - 27 multiples of 3,
31, 32, 39
HOMEWORK HOMEWORK
HOMEWORK HOMEWORK
HOMEWORK
HOMEWORK HOMEWORK
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Section 8.P
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