Tell whether the equation represents direct variation.

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Presentation transcript:

Tell whether the equation represents direct variation. Example 1 Identifying Direct Variation from an Equation Tell whether the equation represents direct variation. a. – 2x + y = b. – 2x + y = 3 SOLUTION Solve each equation for y. y 2x = + – a. 2x y = The equation can be written in the form where k 2, so it represents direct variation. = y kx

The equation cannot be written in the form , Example 1 Identifying Direct Variation from an Equation b. – 2x + y = 3 2x y = + 3 The equation cannot be written in the form , so it does not represent direct variation. = y kx 2

Tell whether the table represents direct variation. Example 2 Identifying Direct Variation from a Table Tell whether the table represents direct variation. a. x 1 2 3 4 5 y 6 10 14 18 22 b. y x 3 2 1 4 5 8 12 16 20 SOLUTION For each table, determine whether the ratios of y to x are constant. 3

Because , the ratios are not constant. So, Example 2 Identifying Direct Variation from a Table Because , the ratios are not constant. So, the table does not represent direct variation. = 1 6 2 10 a. Because , the ratios are constant. So, the table represents direct variation. 3 12 1 4 2 8 = 16 5 20 b. 4

Graph the equation from part (a). What does the slope represent? Example 3 Using Direct Variation BUYING CDS At a music store sale, the amount y (in dollars) that you spend varies directly with the number x of CDs that you buy at the sale price. You pay $36 for 3 of the CDs on sale. a. Write a direct variation equation for the situation that relates x and y. Graph the equation from part (a). What does the slope represent? c. Find the cost to buy 7 of the CDs on sale.

Use the fact that y 36 when x 3 to write a direct variation equation. Example 3 Using Direct Variation SOLUTION a. Use the fact that y 36 when x 3 to write a direct variation equation. = = y = kx Write direct variation equation. Substitute 36 for y and 3 for x. 36 = k ( ) 3 12 = k Solve for k. ANSWER A direct variation equation that relates x and y is y 12x. = 6

Make a table of values for the equation y 12x. x 1 2 3 4 5 y 12 24 36 Example 3 Using Direct Variation b. Make a table of values for the equation y 12x. x 1 2 3 4 5 y 12 24 36 48 60 = Plot the points from the table, and draw a line through the points. The slope of the line is 12 and represents the cost (in dollars) per CD. 7

Example 3 Using Direct Variation c. To find the cost of 7 CDs, substitute 7 for x in the equation from part (a). y = 12x Write direct variation equation. Substitute 7 for x. = 12 ( ) 7 = 84 Simplify. ANSWER The cost to buy 7 CDs is $84. 8

Tell whether the equation or table represents direct variation. Guided Practice for Examples 1, 2, and 3 Tell whether the equation or table represents direct variation. 1. 3x y = ANSWER yes 2. y x = + – ANSWER yes 3. 1 y x = + 3 ANSWER no y x 3 2 1 4 6 9 12 4. ANSWER yes

Tell whether the equation or table represents direct variation. Guided Practice for Examples 1, 2, and 3 Tell whether the equation or table represents direct variation. y x 3 2 1 4 8 9 10 11 5. ANSWER no 6. WHAT IF? In Example 3, suppose you want to buy 9 of the CDs that are on sale. How much will this cost? ANSWER $108