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Understanding Direct Variation | Math Lesson 3.1

Learn to identify, write, & graph direct variation equations. Practice problems & explanations provided. Improve math skills now!

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Understanding Direct Variation | Math Lesson 3.1

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  1. Math CC7/8 – April 24 Math Notebook: • Topic: Direct Variation • HW: Worksheet Things Needed Today (TNT): • Pencil/Math Notebook/Calculators/book • TwMM 3.1

  2. What’s Happening Today? • Warm Up – Review Quiz #1 • Lesson 3.1 – Direct Variation

  3. You will be able to identify, write, & graph an equation of direct variation!

  4. Warm Up 1. Regina walked 9 miles in 3 hours. How many miles did she walk per hour? 2. To make 3 bowls of trail mix, Sandra needs 15 ounces of nuts. How many ounces of nuts does she need for 1 bowl of trail mix? 3 mi per hour 5 oz

  5. Direct Variation Direct variation is a linear relationship between two variable that can be written in the form y = kx or k= , where k ≠ 0. The fixed number k in a direct variation equation is the constant of variation.

  6. How to read Direct Variation You can read direct variation as “y varies directly as x” or “y is directly proportional to x” or “y varies with x.”

  7. Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. y + 8 = x Solve the equation for y. Subtract 8 from both sides. y + 8 = x – 8 = – 8 y = x – 8 The equation is not in the form y = kx, so y + 8 = x is not a direct variation.

  8. 3y = 2x 33 23 2x3 y = x 23 Write as x . Identifying a Direct Variation from an Equation Tell whether each equation represents a direct variation. If so, identify the constant of variation. 3y = 2x Solve the equation for y. Divide both sides by 3. The equation is in the form y = kx, so the original equation 3y = 2x is a direct variation.

  9. Y x Find for each ordered pair. y 2 y 4 y 3 1 = = = = x 69 x 129 x 99 33 k is not the same for each ordered pair. The data does not represent a direct variation. Identifying a Direct Variation from a Table Tell whether each set of data represents a direct variation. If so, identify the constant of variation and then write the direct variation equation.

  10. Helpful Hint In a direct variation where k is positive, when x increases, y also increases; when x decreases,y also decreases.

  11. Y x Find for each ordered pair. y y y 2.54 5.08 12.7 = = 2.54 = = 2.54 = = 2.54 x x x 1 2 5 k = 2.54 for each ordered pair. The data represent a direct variation where k = 2.54. The equation is y = 2.54x Identifying a Direct Variation from a Table Tell whether each set of data represents a direct variation. If so, identify the constant of variation and then write the direct variation equation.

  12. Y x Find for each ordered pair. y y y 2 4 3 = = = x x x 5 15 10 k is not the same for each ordered pair. The data does not represent a direct variation. Can you identify, write, and graph an equation of direct variation? Tell whether each set of data represents a direct variation. If so, identify the constant of variation and then write the direct variation equation.

  13. y 4 2 x 0 –2 2 4 –4 –2 –4 Identifying a Direct Variation from a Graph Tell whether each graph represents a direct variation. If so, identify the constant of variation and then write the direct variation equation. The graph is a line through (0, 0). This is a direct variation. The slopeof the line is ½, so k = –½ . The equation is y= -½x.

  14. y 4 2 x 0 –2 2 4 –4 –2 –4 Tell whether the graph represents a direct variation. If so, identify the constant of variation and then write the direct variation equation. The line does not pass through (0, 0). This is not a direct variation.

  15. A truck travels at a speed of 55 miles per hour. Write a direct variation equation for the distance y the truck travels in x hours. distance = 55 miles per hour number of hours times Use the formula y = kx. k = 55 y = 55 ● x y = 55x

  16. A truck travels at a speed of 55 miles per hour. Graph the data. Make a table. Since time cannot be negative, use nonnegative number for I.

  17. Use the ordered pairs top plot the points on a coordinate plane. Connect the points in a straight line. Label the axes. Check y = 55x is in slope-intercept form with m= 55 and b = 0. The graph shows a slope of 55 and a y-intercept of 0. 100 75 Distance (mi)‏ 50 25 6 4 2 8 Time (h)‏

  18. 660 = 55x 5555 How long does it take the truck to travel 660 miles? Find the value of x when y = 660 Write the equation for the direct variation. y = 55x Substitute 660 for y. 12 = x Divide both sides by 55. It will take the truck 12 hours to travel 660 miles.

  19. Tell whether each of the following represents a direct variation. If so, identify the constant of variation. 1. 12y = 6x 2. yes; k = ½ no

  20. Homework: Direct Variation Worksheet

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