Transcript Objective - To solve problems involving direct and inverse variation.

Objective - To solve problems involving
direct and inverse variation.
Direct Variation
Inverse Variation
y  kx
k
y
x
x y
x
y
Let x = price
Let y = profit/unit
Let x = price
Let y = sales
Sales
Profit
Price
Price
Determine whether the equations are examples
of direct variation, inverse variation, or neither.
2
Direct
1) y  x
4) y  10  x Inverse
5 Variation
10 Variation
y  kx
2) xy  7
y
x
Inverse 5) 5  x  y
x x Variation
7
y
x
3) 3  y  x
Neither
y
Neither 6)  x   3 x  Direct
x
Variation
y  3x
If y varies directly with x, use the given values
to write an equation that describes y in terms of x.
2) x = 48 y = 18
1) x = 5 y = 20
y  kx
20  k  5
5
5
4k
y  4x
y  kx
18  k  48
48 48
18
3
k 
48
8
3
y x
8
If y varies inversely with x, use the given values
to write an equation that describes y in terms of x.
2) x = 3 y = 15
1) x = 12 y = 4
k
k
y
y
x
x
k
k
12 4  12
315  3
12
3
48  k
48
y
x
45  k
45
y
x