Direct Inverse Variations EQ How can you recognize

Direct Variations y = kx where k is the constant of variation Examples of

Did you know… A direct variation can also be called a A direct proportion

Direct Proportions Inverse Proportions Direct Variation Inverse variation As x increases, Y increases or

Compare the equations… Direct Inverse Y = kx Y = k/x Compare the graphs…

Direct, Inverse, or neither? 1. Y = 2 x 2. Y = 10/x 3.

Now that you know the formula for direct and inverse, can you write the

Look at pages 314 & 315 in your book. Read pg. 314 Do pg.

pg. 315 continued 3. y = ____ Now graph it. 4. Make an xy

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

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Direct & Inverse Variations 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 Variations y = kx where k is the constant of variation Examples of direct variations: y = 2 x y = 4 x y = 1/2 x y = -3 x Consider this linear equation: y = 2 x – 1 Compare a direct variation with the linear equation: What’s the difference? Y = 2 x compared with y = 2 x - 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 Inverse Proportions Direct Variation Inverse variation As x increases, Y increases or decreases at a CONSTANT RATE Y decreases (But the rate may not be constant).

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 = 2 x 2. Y = 10/x 3. Y = -. 5 x 4. Y = 2 x + 1 5. Y = 3 x – 8 6. Y = 10 x 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. 315 1. k = Then graph it. 2. Missing width = ____ Now graph

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

Pg. 315 continued 5. Write an inverse variation for k=30, k=20, and k=10 ________, _____ x y x y