EQ: How can you recognize a direct variation equation? EQ: How can you recognize an inverse variation equation? a direct variation graph? an inverse variation.

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Presentation transcript:

EQ: How can you recognize a direct variation equation? EQ: How can you recognize an inverse variation equation? a direct variation graph? an inverse variation graph? Direct & Inverse Variations

Direct Variations y = kx where k is the constant of variation Examples of direct variations: y = 2xy = 4xy = 1/2xy = -3x Consider this linear equation: y = 2x – 1 Compare a direct variation with the linear equation: What’s the difference? Y = 2xcompared with y = 2x - 1

Did you know… A direct variation can also be called a A direct proportion Some books / tests will say direct variation While others will say direct proportion. Be aware of both terms.

Direct Proportions Direct Variation As x increases Y increases or decreases at a CONSTANT RATE Inverse variation As x increases, Y decreases (But the rate may not be constant). Inverse Proportions

Compare the equations… Direct Inverse Y = kx Y = k/x Compare the graphs… Direct variation graphs always go through the __________. Inverse variation graphs are curves that will never quite reach the axes.

Direct, Inverse, or neither? 1.Y = 2x 2.Y = 10/x 3.Y = -.5x 4.Y = 2x Y = 3x – 8 6.Y = 10x 7.Y = 12/x 8.Y = 13/x

Now that you know the formula for direct and inverse, can you write the equation for each if given k? If x & y vary directly, write an equation if k = 4 Y = kx so, if k=4 ___________ If x & y vary directly, write an equation if k = 10 Y = kx so, if k=4 ___________ If x & y vary directly, write an equation if k = -3 Y = kx so, if k=4 ___________ If x & y vary INVERSELY, write an equation if k = 4 Y = k / x so, if k = 4 ___________ If x & y vary INVERSELY, write an equation if k = 10 Y = k / x so, if k = 4 ___________ If x & y vary INVERSELY, write an equation if k = -3 Y = k / x so, if k = 4 ___________

Look at pages 314 & 315 in your book. Read pg. 314 Do pg k = Then graph it. 2. Missing width = ____ Now graph

pg. 315 continued 3. y = ____ Now graph it. 4. Make an xy chart for Graph them here y = 1x y = 2x y = 3x xyxy xy

Pg. 315 continued 5. Write an inverse variation for k=30, k=20, and k=10 ________, ________, _________ xy xyxy