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Understanding Direct Variation Equations: Learn, Identify, Graph

Explore direct variation relationships, equations, and graphing to enhance your math skills. Practice identifying constants of variation and solving for variables. Improve your graphing abilities with practical examples.

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Understanding Direct Variation Equations: Learn, Identify, Graph

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  1. Learning Target Students will be able to: Identify, write, and graph direct variation.

  2. A recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a chef needs 1 cup of rice for every 5 servings.

  3. A direct variation is a special type of linear relationship that can be written in the form y = kx, where k is a nonzero constant called the constant of variation.

  4. Tell whether each equation represents a direct variation. If so, identify the constant of variation. y = 3x 3x + y = 8 –4x + 3y = 0

  5. So, in a direct variation, the ratio is equal to the constant of variation. What happens if you solve y = kx for k?

  6. Tell whether the relationship is a direct variation. Explain.

  7. Tell whether each relationship is a direct variation. If it is, explain.

  8. The value of y varies directly with x, and y = 3, when x = 9. Find y when x = 21.

  9. A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph. distance (mi)

  10. The perimeter y of a square varies directly with its side length x. Write a direct variation equation for this relationship. Then graph. Perimeter HW pp. TBD

  11. Learning Targets Write a linear equation in slope-intercept form. Graph a line using slope-intercept form.

  12. Graph the line given the slope and y-intercept. y intercept = 4

  13. slope = 4; y-intercept = Graph the line given the slope and y-intercept.

  14. Graph the line given the slope and y-intercept. slope = 2, y-intercept = –3

  15. Graph the line given the slope and y-intercept. slope = , y-intercept = 1

  16. slope = ; y-intercept = 4 Write the equation that describes the line in slope-intercept form.

  17. Write the equation that describes the line in slope-intercept form. slope = –9; y-intercept =

  18. Write the equation that describes the line in slope-intercept form. slope = 2; (3, 4) is on the line

  19. Graph the line described by the equation. y = 3x – 1

  20. Graph the line described by the equation. 2y + 3x = 6

  21. HW pp. 329/10-34 even & pp. 338-340/13-29,31 Graph the line described by the equation. y = –4

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