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# Algebra graphs and functions 4 4 4-5

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### Algebra graphs and functions 4 4 4-5

1. 1. Writing a Function Rule and Direct Variation Chapter 4 Lesson 4-4 and Lesson 4-5
2. 2. Function Rules <ul><li>You can write a rule for a function by analyzing a table of values. Look for a pattern relating the Independent and dependent variables. </li></ul>
3. 3. Writing a Rule form a Table <ul><li>Function Table </li></ul>8 4 7 3 6 2 5 1 f (x) x
4. 4. Write rules for the following tables <ul><li>Remember to look for a pattern </li></ul>2 4 1 3 0 2 -1 1 f(x) x 4 8 3 6 2 4 1 2 x y
5. 5. Application <ul><li>A carpenter buys finishing nails by the pound. Each pound of nails costs \$1.19. </li></ul><ul><li>Write a function rule to describe this relationship. </li></ul><ul><li>How much do 12 lb of finishing nails cost? </li></ul>
6. 6. Direct Variation <ul><li>A function in the form y= kx , where k ≠0, is a direct variation . The constant of variation for direct variation k is the coefficient of x. The variables y and x are said to vary directly with each other. </li></ul>
7. 7. Direct Variation <ul><li>For y = kx, y is a function of x. If x = 0, then y = 0, so the graph of a direct variation is a line that passes through (0,0). </li></ul><ul><li>To tell whether an equation represents a direct variation. Solve for y. </li></ul><ul><li>If the equation can be written in the form “ y = kx” , where k ≠ 0, it represents a direct variation. </li></ul>
8. 8. Is an equation a Direct Variation? <ul><li>Is each equation a direct variation? If it is, find the constant of variation. </li></ul><ul><li>What form should the equation take? </li></ul><ul><li>5x + 2y = 0 7y = 2x </li></ul><ul><li>5x + 2y = 9 3y + 4x = 8 </li></ul>
9. 9. Writing an Equation Given a Point <ul><li>Write an equation of the direct variation that includes the point (4,3) . </li></ul><ul><li>First start with the function form of a direct variation : y=kx </li></ul><ul><li>Substitute 4 for x and -3 for y </li></ul><ul><li>Solve for k </li></ul><ul><li>Write an equation. Substitute the solution for k in the equation y=kx </li></ul>
10. 10. Application Real-World Situation <ul><li>Your distance from lighting varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see lighting, you are about 2 miles from the lighting. Write an equation for the relationship between time and distance. </li></ul>
11. 11. Proportions and Equations of Direct Variations <ul><li>You can rewrite a direct variation y = kx as y/x = k. When two sets of data vary directly, the ratio y/x is the constant of variation. It is the same for each data pair. </li></ul>
12. 12. Direct Variation and Tables <ul><li>For the table use the ratio y/x to tell whether y varies directly with x. If it does, write an equation for the direct variation. </li></ul>15 10 12 8 6 4 y/x y x
13. 13. Sum it up <ul><li>Write a function rule for the table </li></ul>-1 2 -2 1 -3 0 -4 -1 f(x) x
14. 14. Sum it up <ul><li>State the form of a direct variation rule. </li></ul><ul><li>What does the k represent? </li></ul><ul><li>State the form of a direct variation proportion. </li></ul><ul><li>Is each equation a direct variation? I t it is, find the constant of variation. </li></ul><ul><li>x + 5y = 10 and 3y + 8x = 0 </li></ul><ul><li>Write an equation of the direct variation that includes the point (-5,-4) </li></ul>