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Warm-Up

Warm-Up. Write in function form 8x - 2y =14 3x + y = 0 Find the x and y intercepts of y=x+8. Find the slope of the line between the two points (4, 3) and (6, 2). Direct Variation. SWBAT identify when two variables vary directly. SWBAT write equations for direct variation. Direct Variation

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Warm-Up

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  1. Warm-Up • Write in function form • 8x - 2y =14 • 3x + y = 0 • Find the x and y intercepts of y=x+8. • Find the slope of the line between the two points (4, 3) and (6, 2).

  2. Direct Variation SWBAT identify when two variables vary directly. SWBAT write equations for direct variation.

  3. Direct Variation A linear line that goes through (0,0) So what does the equation look like?

  4. Direct Variation • K is a number called the constant of variation (but it’s just your slope!)

  5. Is the equation a direct variation? If it is, find the constant of variation. Is the equation a direct variation? Yes, it’s in the form y=kx. What is the constant of variation? k= ¼

  6. Is the equation a direct variation? If it is, find the constant of variation. Is the equation a direct variation? No, it does not have a y-intercept of zero. It is not of the form y=kx.

  7. Is the equation a direct variation? If it is, find the constant of variation. Is the equation a direct variation? Yes, it can be written in the form y=kx. What is the constant of variation? k=-3

  8. Is the equation a direct variation? If it is, find the constant of variation. Is the equation a direct variation? No, it can not be written in the form y=kx.

  9. Graphs of Direct Variation • The graph of y=kx is a line through the origin

  10. Example • In the graph below, do x and y have direct variation?

  11. Example • In the graph below, do x and y have direct variation?

  12. Finding K • K can be found using just one ordered pair!

  13. Using Direct Variation • y varies directly with x and y=24 when x=12, write an equation that models this direct variation. • “y varies directly with x” implies y=kx • Step 1: Find K • Step 2: Write an equation

  14. Using Direct Variation • “y varies directly with x”. If y=8 when x= 12, find X when y=1. • “y varies directly with x” implies y=kx • Step 1: Find K • Step 2: Write an equation • Step 3: Plug y=1 into equation and solve for x

  15. Using Direct Variation • The amount of blood in a person’s body varies directly with body weight. A person who weighs 160 lbs. has about 5 qt of blood. • Find the constant of variation • Write an equation relating quarts of blood to weight • How many quarts of blood would you have in your body if you weighed 200 lbs?

  16. Using Ratios to Model Direct Variation • The model y=kx can be rewritten as follows • The ratio form tells you that if x and y have direct variation then the ratio of y to x is the same for all x and y.

  17. Tell whether y varies directly with x. If so, write an equation for the direct variation. First, check to make sure k is constant (Remember ) K is constant so y varies directly with x. y = 2x is the equation!

  18. Tell whether y varies directly with x. If so, write an equation for the direct variation. First, check to make sure k is constant (Remember ) K is NOT constant so there is no direct variation.

  19. Homework • Worksheet

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