direct and inverse variation day 2 the general equation for direct variation is k is called the...
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Direct and Inverse Variation
Day 2
y =kx with k≠0.
The general equation for direct variation is
k is called the constant of variation.
General Equation
If y varies directly as x, and y=24 and x=3 find the constant of variation.
y=kx24=k⋅3k=8
Example
Exampley varies directly as x, and x=8 when y=9. Find the constant of variation.
y = kx
9 = 8k
k = 9/8
y varies directly as x, and x=8 when y=9. Find y when x = 4.
Use the formula for direct variation.
Y = 4.5
Example
Inverse Variation
y varies inversely as x if k≠0
such that xy=k or
y=kx
Just as with direct variation, a proportion can be set up solve problems of indirect variation.
Indirect Variation
Lets do an example that can be solved by using the equation and the proportion.
x1y1 =x2y2
Solve:
Find x when y=27, if y varies inversely as x and x=9 when y=45.
Answer: 15
Determine if the chart is a direct variation
• To solve, find the constant of variation for each pairing of numbers using the formula y=kx.
• YES! The constant of variation is 2.
x 10 12 14 16 18
y 20 24 28 32 36
Determine if the chart is a direct variation
• To solve, find the constant of variation for each pairing of numbers using the formula y=kx.
• YES! The constant of variation is 1/2.
x 20 16 12 8 4
y 10 8 6 4 2
Determine if the chart is a direct variation
• To solve, find the constant of variation for each pairing of numbers using the formula y=kx.
• NO! The constant of variation is changes and is not the same for all pairs.
x 6 9 15 18 24
y 2 3 5 9 12
Determine if the charts are direct variationsx 2 8 9 14 18
y 6 24 27 42 54
x -3 9 15 18 -21
y -2 6 10 12 -14
x -1 3 5 8 10
y -2 6 10 12 -14