I can write and graph an equation of a direct variation by identifying the constant of variation.

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Presentation transcript:

I can write and graph an equation of a direct variation by identifying the constant of variation.

Direct Variation

Identifying a Direct Variation

Graphing a Direct Variation  Solve for the constant of variation.  Write an equation.  Make a table of values.  Graph the ordered pairs.  Connect the points if necessary.  The line always passes through (0,0)

Writing a Direct Variation  Suppose y varies directly with x, and y = 35 when x = 5. What direct variation equation relates x and y?  A direct variation is of the form: y = kx  So, 35 = k(5)  Solve for k by division: 7 = k  Write an equation using 7 for k: y = 7x

From a Table

Using a Proportion

Using Direct Variation to Solve  A salesperson’s commission varies directly with sales. For $1000 in sales, the commission is $85. What is the commission for $2300 in sales?  Y varies directly with x (y=kx) but in this case commission c varies directly with sales s.  So we can say c = ks.  Find k: 85 = k(1000)  K =  Now find the commission when s = 2300  C=0.085(2300)  C = so the commission is $195.50

Assignment  Odds  P. 71 #7-13,19-27,35