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Understanding Direct Variation and Linear Functions in Graphs

Dive into the principles of linear relations and direct variation with our engaging lesson. Learn how to analyze the characteristics of graphs including constant functions, direct variation, and absolute values of linear functions. You'll apply technology to enhance your learning experience. Key concepts include calculating the slope of a line, predicting resource usage in everyday scenarios, and determining the constant of variation for linear equations. This lesson is designed to boost your mathematical skills and encourage innovative thinking!

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Understanding Direct Variation and Linear Functions in Graphs

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  1. Bellwork Never tell people how to do things. Tell them what to do and they will surprise you with their ingenuity.George S. Patton

  2. CFU3102.1.18 Analyze the characteristics of graphs of basic linear relations and linear functions including constant function, direct variation, identity function, vertical lines, absolute value of linear functions. Use technology where appropriate. 3.4 Direct Variation

  3. Bellwork

  4. Using Slope • Use the two points to calculate slope of the line. • Using Slope can you predict the gallons used in a 5 minute shower, a 10 minute shower?

  5. Using Slope • Use the two points to calculate slope of the line. Y2 –Y1 18 - 6 12 m= m= m= X2 –X1 3 - 1 2 m= 6

  6. Using Slope • Using Slope can you predict the gallons used in a 5 minute shower, a 10 minute shower? X- 18 X- 18 X- 18 Y2 –Y1 60 = X 6= 12 = X- 18 48 = X- 18 6= m= 6= X2 –X1 5 - 3 2 10 - 3 30 = X

  7. Direct Variation • If y varies directly with x • Equation y = k x • k is constant of variation • When Graphed, k is same as m (slope)

  8. Determine the direct Variation of a Line • If y = kx and k is the constant of variation • What is the constant of variation for • y = 3x • What about • x = -88x With Direct Variation y = k x

  9. What is the Constant of Variation if • Find the constant for the given line, write the direct variation equation 20 30–10 Y2 –Y1 Y2 –Y1 k=m= k=m= k=m= m= 4 6 –2 X2 –X1 X2 –X1 Y (6, 30) (2, 10) k=m= 5 y = kx y = 5x X With Direct Variation y = k x

  10. Find missing variable • If y varies directly with x • Write an equation for when y = 28 and x = 7 • Then solve for x when y = 52 • 28 = k (7) • k = 4 • y = 4x • Now solve for x given y = 4x • 52 = 4x • x = 13 • x = 2, y = ? • y = 8 Y X With Direct Variation y = k x

  11. Find missing variable • If y varies directly with x • Write an equation for when y = 9 and x = -3 • Then solve for y when x = -5 • 9 = k (-3) • k = -3 • y = -3x • Now solve for y given y = -3x and x = -5 • y=-3(-5) • x = 15 With Direct Variation y = k x

  12. Practice Assignment • Page 183, 10 - 36 Even

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