Direct and Joint Variation Chapter 4 Section 3 Direct and Joint Variation

Essential Question When collecting data, you might see a pattern. What types of things are related directly?

Direct Variation Direct variation: as one quantity increases (or decreases) the other quantity also increases (or decreases) Uses independent variable (x), dependent variable (y) and constant of variation (k) Similar to a linear function that has a y- intercept of 0 (goes through origin)

Direct variation example When one value is cut in half, what happens to the other one? When one value is doubled, what happens to the other one? What would the graph look like? What is the constant of variation?

Practice with direct variation (1-35) A blueprint has a scale of 0.5 in. = 1 ft. On a blueprint a wall is drawn to be 7.5 in. long. What is the actual measure of the wall? A 10-in. diameter gear is in mesh with a 5- in. diameter gear. If the larger gear has a speed of 25 rpm, how many rpm does the smaller gear turn?

Practice with direct variation (1-35) If 6 cans of coffee sell for $22.24, how much will 20 cans sell for? A costume maker took 9 h to make 4 headpieces for a Mardi Gras ball. At this rate, how many complete headpieces can be made in 35 h? A roof has a pitch of 1:3. If the span is 42 ft., what is the rise? (rise is height and span is length)

Joint Variation (47-49) y = kxz “y varies jointly as x and z” Example: Find w if w varies jointly as x and y and x = 140, y = 6, and the constant of joint variation is 0.5