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Direct Variation. y = kx. A direct variation is…. A linear function Equation can be written in the form; y = mx ; m 0 or y = kx ; k 0 The y-intercept must be zero!!!! Graphs a line passing through the origin. Constant of Variation: y = k x.

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## Direct Variation

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**Direct Variation**y = kx**A direct variation is…**• A linear function • Equation can be written in the form; y = mx ; m 0 or y = kx ; k 0 • The y-intercept must be zero!!!! • Graphs a line passing through the origin.**Constant of Variation: y = kx**• The constant of variation is the rate of change for data that describes the variation (slope). • The constant of variation is found by dividing “y” by “x” (k = y/x) • The constant of variation is the slope of a linear equation whose y-intercept is zero!!!!**Constant of Variation: y = kx**y= x k= 1 y= 2x k= 2 y= x k= y= x k= y= -x k= -1**Which is a direct variation?**For an equation to be that of a direct variation: #1) Put equation into “y=“ form. #2) Check out equation: y = kx + 0 or y= kx no • 1. y = 3x + 2 • 2. y = 2x • 3. 3x – y = 0 • 4. 9x + 3y = -3 • 5. 2x + 3y = 0 • 6. yes yes no yes yes**Example 1**• The distance that you travel at a constant speed varies directly with the time spent traveling. It takes you 2 hours to travel 100 miles. How long will it take you to travel 400 miles? • Direct variation: y varies directly as x y = k x • This problem: distance varies directly as time d = k t**Example 1 (cont.)**This problem: distance varies directly as time d = k t Write an equation for the relationship between the time and distance. Find “k” first using the given ordered pair (time, distance) …. (2, 100) 100 = k (2) 50 = k Thus the equation for this problem: d = 50 t**Example 1 (cont.)**Now this equation can be used to find any number of distances or times. equation :d = 50 t How long will it take you to travel 400 miles? 400 = 50 t How long will it take you to travel 750 miles? 750 = 50 t How many miles could you travel in 3.5 hours? d = 50 (3.5)**Example 2**• The money you earn varies directly with the number of lawns you mow. You earn $36 for mowing 3 lawns. • Write an equation for the relationship between money earned and lawns mowed. • How much money would you earn for mowing seven lawns? • How many lawns did you mow for $60? Equation: m = 12L Equation: m = 12(7) Equation: 60 = 12L**Suppose the ordered pairs in each problem are for the same**direct variation. Find the missing value. Slope is constant: 1st) given two ordered pairs: (x,y) & (x,y) 2nd)k = y/x 3rd)y/x = y/x 4th) solve the proportion for the unknown • 1. (4, 2) and (6, y) 2/4 = y/6 • 2. (2, 7) and (x, 3) 7/2 = 3/x • 3. (x, 9) and (1.4, 2.8) 9/x = 2.8/1.4 • 4.**k =**y = x k = Write a direct variation equation for the following: y = kx (2,5) (0,0)

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