1.4 Direct Variation and Proportion

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1.4 Direct Variation and Proportion

• Objectives Write and apply direct variation
  equations. Write and solve proportions.
• Standard 2.8.11.P Analyze a relation to
  determine whether a direct or inverse variation
  exists and represent it algebraically and
  graphically.

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I. Determine whether each equation describes a
direct variation.

• Direct Variation - The variable y varies
  directly as x.
• y kx is known as a direct-variation
  equation.
• k is called the constant of variation.

y 2x
yes
y ½ x
yes
y 2x 1
no
y 3/x
no
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II. y varies directly as x. Find the constant
of variation, k, and write an equation of direct
variation that relates the two variables, y kx.

• 1. y -24 when x 4
• 2. y -16 when x 2
• 3. y 1 when x ½

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III. y varies directly as x.

1. If y is 2.8 when x is 7, find y when x is -4.
2. If y is 6.3 when x is 70, find y when x is
5.4.

• 3. If y is -5 when x is 2.5, find y when x is 6.

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IV. Use a direct variation equation to solve
each word problem.

• 1. If 6 tickets cost 72, find the cost of 10
  tickets.

72 k (6)
12 k
y 12 (10) y 120
2. If 3 CDs on sale cost 18, find the cost of
12 CDs.

• 3. If 8 sodas cost 3.20, find the cost of 20
  sodas.

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IV. Use a direct variation equation to solve
each word problem.

• Ex 4. Each day Jon rides his bicycle for
  exercise. When traveling a constant rate, he
  rides 4 miles in about 20 minutes. At this rate,
  how long would it take Jon to travel 7 miles?
  Recall that distance, d, rate, r, and elapsed
  time, t, are related by the equation d rt.

Rate 4 miles/20 minutes 1/5 miles per minute
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V. Proportions

• If y varies directly with x, then y is
  proportional to x.
• A proportion is a statement that two ratios are
  equal.
• A ratio is the comparison of 2 quantities by
  division.
• A proportion of the form a c can be rearranged
  as follows
• b
  d
• a c
• b d
• a ? bd c ? bd
• b d
• ad bc

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V. Proportions

• Cross-Product Property of Property of
  Proportion
• For b ? 0 and d ? 0 If a c, then ad bc.
  b d
• In a proportion of the form a/b c/d a and d
  are the extremes and b and c are the means.
• By the Cross-Product Property, the product of
  the extremes equals the product of the means.
  

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V. Proportions

• 2. 3 x
• 5 2

• 1. w 10
• 4 12

• 3. 3x 1 x
• 5 2

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Ex. 4 Proportions
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Homework

• Integrated Algebra II- Section 1.4 Level A even
  s
• Honors Algebra II- Section 1.4 Level B