1. Warm-Up 2 1.Solve for y: 2x + y = 6 2.Solve for y: 2x + 3y = 0

2. Anyone have a Job where you get paid by the hour?

3. Direct Variation A function in the form y = kx, where k is the constant of variation. (*** K is the SLOPE***) The variables y and x, “ vary directly”! If The equation looks like y = kx, then it is DIRECT VARIATION!

4. Is it DV? Is the equation Direct Variation? –Identify the constant k in each equation if it represents direct variation. 1.Y = 3x2. Y = 4x + 1

5. 3. Y = x4. 2y = 8x 5. 5x + 2y = 06. 3x – y = 7

6. More facts about Direct Variation If the graph goes through the point (0,0), then it is DIRECT VARIATION! 1: Which graphs are direct variation?

7. 2. Are these direct variation? a) b) c)

8. Writing a Direct Variation Equation Write a direct variation through the point (4, -3). Ex. 1: Write an equation of the direct variation that includes the point: (4, -3) Step1: Start with the direct variation equation: Step 2: Substitute the x and y in the ordered pair for the x and y in the equation. Step 3: Solve for k. Step 4: Write the equation substituting the value in step 3 for k in the equation

9. You try! 2. Write a direct variation through the point (5, 2) 3. Write a direct variation through the point (-6, -6) 4. Write a direct variation through the point (-3, -12)

10. Determine if a table varies directly… *The k value must be the same for each ordered pair* To find k:

11. 3. Direct Variation in a Table Do the tables vary directly? a)b)

12. Do the values vary directly?

13. Proportions can also be used to solve DVs