5.3 direct variation c
TRANSCRIPT
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Direct Variation Equations
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ReviewWhat is the slope?
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Slope = 1/2
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Slope = -1
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Slope = 5
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Slope = Undefined
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65 mph
1. What was the greatest speed that Michael traveled?
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Constant Speed
2. What does the horizontal segment of the graph represent? How long does Michael stay at this speed?
70 mins - 20 mins = 50 mins
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Speed is decreasing
3. What does the segment with a negative slope tell you about Michael’s speed?
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Speed is increasing
4. What does the segment with a positive slope tell you about Michael’s speed?
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Vocabulary
• Direct Variation Equation – An equation of the form y = kx, where k does not equal zero
• Constant of Variation – k in a direct variation equation
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Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.
Slope formula
Simplify.
Answer: The constant of variation is 2. The slope is 2.
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Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points.
Slope formula
Simplify.
Answer: The constant of variation is –4. The slope is –4.
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Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
a. Answer: constant ofvariation: 4; slope: 4
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Answer: constant ofvariation: –3; slope: –3
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
b.
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• The constant of variation is the slope
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Find the value of k.Direct variation formula
15 = k(5) Replace y with 15 and x with 5.
15 = k(5) 5 5 Divide each side by 5
3 = k Simplify
Equation?
y = 3x
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.5. Y = 15 when x = 5
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Find the value of k.Direct variation formula
9 = k(3) Replace y with 15 and x with 5.
9= k(3)3 3 Divide each side by 5
3 = k Simplify
Equation?
y = 3x
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.7. Y = 9 when x = 3
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Find the value of k.Direct variation formula
18 = k(11) Replace y with 15 and x with 5.
18= k(11)11 11 Divide each side by 518 = k Simplify11
Equation?
y = 18x 11
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.9. y = 18 when x = 11
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Find the value of k.Direct variation formula
42 = k(7) Replace y with 15 and x with 5.
42= k(7) 7 7 Divide each side by 56 = k Simplify
Equation?
y = 6x
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.11. y = 42 when x = 7
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Find the value of k.Direct variation formula
12 = k(22) Replace y with 15 and x with 5.
12= k(22)22 22 Divide each side by 56 = k Simplify11
Equation?
y = 6 x 11
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.13. y = 12 when x = 22
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Graph the equation.
The graph of passes through the origin with a slope of 60.
Answer: