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Algebra 1 A Chapter 4 Section 2 Slope and Direct Variation 1 Direct Variation: describes an equation of the form y = kx, where k 0. k is called the constant of variation Key words: Varies directly Examples: y 7.25 x y 12 x always crosses at the point (0, 0) and it is always a straight line. Name the constant of variation of the equation. Then find the slope of the line and write the equation Slope = constant of variation Pick 2 points and find the slope Use the slope formula or the triangle method Slope = 3 y = 3x 2 Example #2 Name the constant of variation of the equation. Then find the slope of the line and write the equation Pick 2 points and find the slope Use the slope formula or the triangle method Slope = -5/2 y = -2.5x Graph the direct variation y = (2/3)x Y= (2/3)x Start at the point( 0, 0) Use the constant of variation to find the next point 3 Ok so if we use y = x as a our parent graph What effect does the constant of variation have on the graph? Calc activity on page 197 ( next slide) 4 Suppose y varies directly as x, and y = 28 when x = 7 a. find the direct variation equation that relates x and y. y = kx 28 = k(7) Substitute 28 for y and 7 for x 4=k So y = 4x b. Use the direct variation equation to find x when y = 52 use y = 4x Substitute 52 for y and solve for x 52 = 4x 13 = x Therefore , x = 13 when y = 52. Travel The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. a. Write the direct variation equation to find distance driven for any number of hours. d = 60t b. Graph the equation Graph left blank on purpose 5 Travel The Ramirez family is driving cross-country on vacation. They drive 330 miles in 5.5 hours. a. Write the direct variation equation to find distance driven for any number of hours. d = 60t b. Graph the equation c. Estimate how many hours it would take them to drive 600 miles. 10 hours 6