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Patterns and Proportional Relationships

Patterns and Proportional Relationships. Standard: M7A3 Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x). Direct Proportion. The table below is a linear function.

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Patterns and Proportional Relationships

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  1. Patterns and Proportional Relationships Standard: M7A3 Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x).

  2. Direct Proportion • The table below is a linear function. One way to describe the function is as x increases by one, y increases by 8. Another way to describe the function is by looking at the ratio y/x in each column of the table. In each column y/x = 8. This can be written as the equation y = 8x Any function (linear table) that can be written as y = kx, where k is a constant, is called a direct proportion.

  3. Direct Proportion in a Graph • How can I determine if a graph is a direct proportion? • 1. The graph of a direct proportion must be a straight line and pass through the point (0, 0). • 2. Pick points on the graph and divide y by x. If the answer is a constant (k) each time, the graph fits the criteria for a direct proportion.

  4. You try it! • Scout earns $12 an hour for each hour she works. Show that a direct proportion exists between the number of hours she works and the amount of money she earns. • Create a table using the information you have. • Write an equation representing the situation. • Does the equation for this problem fit the equation for a direct proportion y = kx ?

  5. Indirect Proportion • An indirect proportion exists when the product (answer you get when you multiply) of two variables is a constant (k). • For example if the variables are x and y, an indirect proportion can be written as xy = k or as y = k/x. • The graph of an indirect proportion will never be a straight line.

  6. Graph the following coordinate pairs • (1, 8) • (2, 4) • (4, 2) • (8, 1) • Is this a direct proportion or indirect proportion? • This graph is typical of an indirect proportion. • What happens when you multiply x and y? • Each product equal 8, thus this is an indirect proportion.

  7. You try it! • Is the function y = 4x + 2 a direct proportion? • 1st step: if x = 1, y = ? (hint: make a table if it helps) • 2nd step: what does this y/x = ? • 3rd step: pick a second point. If x = 2, y = ? What does this y/x = ? • Did you get the same answer for step 2 and 3? If so it is a direct proportion, if not the function is not a direct proportion.

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