This document provides lessons on direct variation, including how to identify direct variation from equations, tables of data, and word problems. It also reviews key characteristics of direct variation: 1) Direct variation is represented by the equation y=kx, where k is the constant of variation and the line always passes through the origin point (0,0). 2) To identify if an equation represents direct variation, isolate y and see if it is in the form y=kx. 3) To determine if a table shows direct variation, calculate the ratio y/x for each pair of values and see if all the ratios are the same.

1. Direct Variation Lesson 5.3

2. Direct Variation Linear function y=kx k cannot be = to 0 Always goes through the origin (0,0) If a line does not go through the origin, it is not direct variation.

3. Constant of Variation The k in the y=kx y/x Rate of change slope

4. Example 1 Is the Equation Direct Variation? Use inverse operations to isolate y. If y=kx, then it is direct variation. If y= anything else, then it is NOT.

6. Example 2 Solve Word Problems Define the independent and dependent variables. Decide how they relate like we did yesterday. Write the equation. Answer the question if there is one.

8. Ex 3 Is the Table Direct Variation? Put each y in a ratio over each x. (y/x) Does each y/x form the same ratio? If yes, substitute the reduced ratio for the k in the equation y=kx .

10. Example 4 Find the missing coordinate? Set up the two points as proportions. y 1 = y 2 x 1 x 2 Fill in what you know. Cross multiply and divide.

11. Review Direct Variation is written in what form? What point does Direct Variation aways go through? How do you know if the equation for a line is direct variation? What steps will you take to solve word problems?

12. Review How do you know if data in a table is direct variation? How do you find a missing coordinate?