Download Inverse Variation - Issaquah Connect

Math CC7/8 – April 25
Things Needed Today (TNT):
Pencil/Math Notebook/Calculators
TwMM 3.2
Math Notebook:
1.Topic: Inverse Variation
2.HW: Worksheet
What’s Happening Today?
Warm Up
Inverse Variation
You will be able to identify, write,
& graph an equation of Inverse
variation!
Warm Up
Find the equation of the line that passes through the given points.
What strategies will you use to find the equation?
(1, 4) and (-2, -2)
y = 2x + 2
Warm Up
Find an equation for the line that satisfies the conditions.
Note: parallel lines have the
SAME slope (m)
Inverse Variation
Inverse Variation is very similar to
direct, BUT in an inverse
relationship as one value goes up,
the other goes down.
Inverse variation is a relationship between two
variables that can be written in the form
y = k/x or xy = k,
where k is a nonzero constant and x ≠ 0.
In an inverse variation, the product of x
and y is constant.
k is the constant of proportionality
Inverse Variation
With Direct variation we Divide
our x’s and y’s.
In Inverse variation we will Multiply our
x’s & y’s.
x1y1 = x2y2
How to read Inverse Variation
You can read inverse
variation as “y varies
inversely with x”.
Inverse Variation
If y varies inversely with x and
y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y
y=3
Inverse Variation
If y varies inversely as x and x = 18 when
y = 6, find y when x = 8.
18(6) = 8y
108 = 8y
y = 27 / 2
What to do if you have a table? Inverse Variation
The product for xy is constant, so the
relationship is an inverse variation with
k = 24.
5(80) = 400
7(75)= 525 9(70) = 630
The product for xy is not constant, so the
relationship is not an inverse variation.
An inverse variation can also be identified by its graph. Since k is
a nonzero constant, ≠ 0. Therefore, neither x nor y can equal 0,
and no solution points will be on the x-axis or y-axis.
Identify Inverse Variation
Tell whether the relationship is an inverse variation.
The table shows how 24 cookies can be divided equally among
different numbers of students.
Number of Students
Number of Cookies
2
3
4
6
8
12
8
6
4
3
2(12) = 24; 3(8) = 24; 4(6) = 24; 6(4) = 24; 8(3) = 24
xy = 24
The relationship is an
The product is always the same.
24
inverse variation: y = x
.
Identify Inverse Variation
Tell whether each relationship is an inverse variation.
The table shows the number of cookies that have been baked at
different times.
Number of Students
12
24
36
48
60
Time (min)
15
30
45
60
75
12(15) = 180; 24(30) = 720
The product is not
always the same.
The relationship is not an inverse variation.
Inverse Variation
Tell whether the relationship is an inverse variation.
x
2
4
8
1
2
y
4
2
1
8
6
2(4) = 8; 2(6) = 12
The product is
not always the
same.
The relationship is not an inverse variation.
Graphing Inverse Variations
Graph the inverse variation function.
x
–4
–2
–1
–
1
2
1
2
1
2
4
y
–1
–2
–4
–8
8
4
2
1
f(x) =
4
x
Graph the inverse variation function.
4
f(x) = –
x
x
y
–4 1
–2 2
–1 4
–
1
2
1
2
8
–8
1
–4
2
–2
–1
4