Constant Rate of Change Sec 7.2-B pg. 392 - 395

Constant Rate of Change A RATE OF CHANGE is a rate that describes how one quantity changes in relation to another. Rate of Change is usually expressed as a unit rate. A CONSTANT RATE OF CHANGE is the rate of change in a linear relationship. Football Tickets Number Cost($) 2 14 4 28 6 42 8 56 +2 +14 +2 +14 +2 +14 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑚𝑜𝑛𝑒𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑐𝑘𝑒𝑡𝑠 = 7 1 14 2 = So the cost of the ticket increases by $7 for each ticket.

Constant Rate of change Look at the graph. To find the rate of change, pick out two points. Let’s use (2, 16) and (4, 32). To find the rate of change. Find the difference in range divided by difference in domain. 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑐𝑜𝑠𝑡 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 = (32 −16) (4 −2) = 16 2 = 8 1 What does the 8 mean? Unit Rate 1 candle cost $8. 8 16 24 32 40 1 2 3 4 5 Cost of Candles Number of Candles

Find the Constant Rate of Change Find the change from row to row. 5 – 2 = 3 $30 - $12 = $18 For the rate of change to be constant from row to row should be the same. 8 – 5 = 3 $48 - $30 = $18 11 – 8 = 3 $66 - $48 = $18 The change in money is $18 each time. The change in hours is 3 each time. Find the unit rate. 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑚𝑜𝑛𝑒𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 ℎ𝑜𝑢𝑟𝑠 = $18 3 = $6 1 The unit rate is $6. Babysiting Money Hours Money 2 $12 5 $30 8 $48 11 $66

Find the constant rate of Change Pick two points. Let’s use (2, 100) and (8, 70) 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒 70 −100 8−2 = −30 6 = −5 1 = - 5 degrees per hour. 120 100 Temperature 80 60- 40 2 4 6 8 10 Hours