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HW – pgs. 109-110 (2-28 even, 32, 33, 35, 39)
www.westex.org HS, Teacher Website
10-2-12
Warm up—ALG 2 CPA
1. Write the equation of a line that is parallel to 3x
+ 2y = -7 and goes through (4,5)?
(Hint: Find the slope first. Is it just 3? NO!!!
Then plug into y – y1 = m(x – x1).)
GOAL:
I will be able to:
1. write and graph direct variation equations.
HW – pgs. 109-110 (2-28 even, 32, 33, 35, 39)
www.westex.org
HS, Teacher Website
Name ______________________
ALG 2 CPA
2.5 Model Direct Variation
Date _______
GOAL:
I will be able to:
1. Write and graph direct variation equations.
Equation
The equation _______________ represents __________ ______________ between x and
y. y is said to ________ ____________ with x. a cannot be zero and is called the
____________ ____ _______________.
Graph
The graph of a direct variation equation y = ax is a _______ with slope ___ and y-intercept
___. All direction variation graphs go through the __________.
Example 1—Write and Graph a Direct Variation Equation
Write and graph a direct variation equation
that has (-3, 6) as a solution.
y
x
YOU TRY:
Write and graph a direct variation equation
that has (6, -2) as a solution.
y
x
Example 2— Write and Apply a Model for Direct Variation
YOU TRY:
The variables x and y vary directly.
The variables x and y vary directly.
Write an equation that relates x and y.
Write an equation that relates x & y.
Then find y when x = 12.
Then find y when x = 5.
x = -4.8, y = -1.2
x = -8, y = 28
Example 3—Use Ratios to Identify Direct Variation
Tell whether the data in the table show direct variation. If so, write an equation relating x & y.
X
-5
-4
-3
-2
-1
Y
20
16
12
8
4
YOU TRY:
Tell whether the data in the table show direct variation. If so, write an equation relating x & y.
X
-8
-4
4
8
12
Y
8
4
-4
-8
-12
Example 4—Write and Apply a Model for Direct Variation-Word Problem
The depth, d, a diver is below the surface of the water varies directly with the time, t, it takes
to ascend to the surface. From a depth of 45 feet it takes a minimum of 0.75 minute for a
safe ascent.
a. Find the constant of variation.
b. Write the direct variation equation that models the depth a person can dive based on the
time it takes to ascend to the surface.
c. What is the minimum time a diver should take to ascend from a depth of 540 feet?
EXIT TICKET
Name _______________________ 10-2-12
Explain why the data in the table show direct variation. Write the direct variation equation.
X
32
16
-16
-32
-48
Y
-8
-4
4
8
12
EXIT TICKET
Name _______________________ 10-2-12
Explain why the data in the table show direct variation. Write the direct variation equation.
X
32
16
-16
-32
-48
Y
-8
-4
4
8
12
EXIT TICKET
Name _______________________ 10-2-12
Explain why the data in the table show direct variation. Write the direct variation equation.
X
32
16
-16
-32
-48
Y
-8
-4
4
8
12
EXIT TICKET
Name _______________________ 10-2-12
Explain why the data in the table show direct variation. Write the direct variation equation.
X
32
16
-16
-32
-48
Y
-8
-4
4
8
12
EXIT TICKET
Name _______________________ 10-2-12
Explain why the data in the table show direct variation. Write the direct variation equation.
X
32
16
-16
-32
-48
Y
-8
-4
4
8
12