1. Holt CA Course 1 7.9 Direct Variation pg. 357 Warm Up Tell whether the ratios are proportional. 1. 2. 3. 4. 6 9 24 36 56 68 14 17 12 13 60 78 40 6 30 4 ? ? ?? = = = = *AF4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation. Tip: Constant Direct Variation: y = kx LO: I will evaluate, graph, & compare direct variation using either tables, proportions, or the equation y = kx.

2. Holt CA Course 1 A direct variation shows a direct relationship between the changes in variables. k = SLOPE!!!! y=kx y x =k (constant of variation). 1.Linear Function (straight line). 2. Must pass through the origin (0,0). Direct Variation:

3. Holt CA Course 1 Determine whether the data set shows direct variation. Method 1: Make a graph. The points lie in a ________ line. (0, 0) is included. Method 2: Compare ratios. 25 10 50 20 75 30 100 40 === y x = y x x y Both methods show the relationship is a ______ ____________. The ratio is constant.

4. Holt CA Course 1 Determine whether the data set shows direct variation. Method 1: Make a graph The graph is not _______. Method 2: Compare ratios. 22 3 27 12 = ? ___ __ = ___ ? Both methods show the relationship is not a _______ ______________. y y y x x = x

5. Holt CA Course 1 Rachel rents space in a salon to cut and style hair. She paid the salon owner $24 for 3 cut and styles. Write a direct variation function for this situation. If Rachel does 7 cut and styles, how much will she pay the salon owner? y = kx ____= k  ___ ___= k y = ___x The amount owed varies directly with the amount of cuts given. Now substitute 8 for k in the original equation. x = ___ and y = ____ Step 1 Write the direct variation function. Undo the multiplication. Step 2 Find how much Rachel will pay the salon owner for 7 cuts and styles. y = 8(__) y = ___ Rachel will pay the salon owner $___ for 7 cut and styles. Recall!! X –input determines Y-output!!

6. Holt CA Course 1 1. 2. Amount of Water in a Rain Gauge Time (h)12345 Rain (in)246810 Driving Time Speed (mi/h)3040506080 Time (h)107.5653.75 3. Roy’s income varies directly with the number of dogs that he walks. He earned $8.50 for walking 2 dogs. Write a direct variation function for this situation. If Roy walks 5 dogs, how much will he earn? (Use: y=kx) HW 7.9p360 #4-12e & SRe Determine whether the data sets show direct variation. 1 2 3 4 5 TIME (h) 5432154321 RAIN (in) = OR = ____direct variation