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## Direct

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**Direct**Inverse joint**The general equation for DIRECT VARIATION is**k is called the constant of variation. We will do an example together.**If y varies directly as x, and y=24 and x=3 find: (a) the**constant of variation (b) Find y when x=2 (a) Find the constant of variation Write the general equation Substitute**(b) Find y when x=2**First we find the constant of variation, which was k=8 Now we substitute into y=kx.**Another method of solving direct variation problems is to**use proportions. Therefore...**So lets look at a problem that can by solved by either of**these two methods.**If y varies directly as x and y=6 when x=5, then find y when**x=15. Proportion Method:**Now lets solve using the equation.**Either method gives the correct answer, choose the easiest for you.**Now you do one on your own.**y varies directly as x, and x=8 when y=9. Find y when x=12. Answer: 13.5**What does the graph y=kx look like?**A straight line with a y-intercept of 0.**y varies inversely as x if**such that xy=k or Just as with direct variation, a proportion can be set up solve problems of indirect variation. Inverse Variation**A general form of the proportion**Lets do an example that can be solved by using the equation and the proportion.**Find y when x=15, if y varies inversely as x and x=10 when**y=12 Solve by equation:**Solve this problem using either method.**Find x when y=27, if y varies inversely as x and x=9 when y=45. Answer: 15**Joint Variation**For three quantities x, y and z, if there is a constant k such that z = kxy We say “z varies jointly as y and x” or “z is jointly proportional to x and y”.**A general form of the proportion**Lets do an example that can be solved by using the equation and the proportion.**Example 9**• U varies jointly as V and the square of W. if V =4 and W = 3, then U = 18. Find the value of V when U = 24 and W = 3.**Class work…**• Work book page 123 and 124 even