1. Slope and Direct Variation Mr Smith

2. By the end of this…  You should know what direct variation is, why it is important, and how you could use it.  You should know what direct variation and slope have in common.  You should be able to answer questions relating y and x, and use equations in direct variation to your advantage when graphing problems.

3. Well, what is direct variation?  It’s in the form y=kx, and k=0. we say y varies directly with x, or y is proportionate to x. The k is what relates them, it is the multiplier.  k is the same number all the time, it is constant. And so, it is the same as slope.  When you graph direct variation, notice the x and y-intercepts are both zero. It graphs through the origin.

4. Name the constant (slope) in these 2 problems:

7. Name the constant (slope) in these 2 problems and write the equation of the line:

11. You can find the constant by knowing what y and x are:  If y is 35 when x is 7, what equation could you write? Remember y is the total.

12. You can find the constant by knowing what y and x are:  If y is 35 when x is 7, what equation could you write? Remember y is the total. y = kx y = 7x  Now that you have the equation in direct variation form, you can plug in something for x and solve for y. If x = 6 solve for y.

13. You can find the constant by knowing what y and x are:  If y is 35 when x is 7, what equation could you write? Remember y is the total. y = kx y = 7x  Now that you have the equation in direct variation form, you can plug in something for x and solve for y. If x = 6 solve for y. y = 7x y = 7(6)y = 42

14. Try these 2 problems. Write a direct variation equation that relates x and y. then solve.  If y = 27 when x = 6, find x when y = 45

15. Try these 2 problems. Write a direct variation equation that relates x and y. then solve.  If y = 27 when x = 6, find x when y = 45 27 = k(6) y = 4.5x 6 6 4.5 = k 45 = 4.5x y = 4.5k 4.5 4.5 10 = x

16. Texbook Problem:

17. Textbook Problem: