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4.2 Rate of Change Notes and Practice Name_______________________ To find the rate of change between two quantities, divide the difference in the y-coordinates by the difference in the corresponding x-coordinates. The coordinates will look like this: (x1 , y1), (x2 , y2) The subscript 1 is for the first ordered pair and the subscript 2 is for the second ordered pair. The formula to find the rate of change looks like this: y2 - y1 ____________ x2 - x1 Notice that the values of the first ordered pair are subtracted from the second ordered pair. When you have a _______________ rate of change, these statements are true: As one quantity(x) _____________, the other quantity(y) _____________. As one quantity(x) _____________, the other quantity(y) _____________. This is how it looks in a table: x y 0 0 1 2 4 8 This is how it looks in a graph This is how it looks in an equation y = 2x When you use the formula to find the rate, it will look like this: How? : Pick 2 ordered pairs, then find the difference between the y-coordinates by the difference between the x-coordinates Try points ( , ) and ( , ) When you have a _______________ rate of change, these statements are true: As one quantity(x) _____________, the other quantity(y) _____________. As one quantity(x) _____________, the other quantity(y) _____________. This is how it looks in a table: x y 0 8 2 4 3 2 This is how it looks in a graph This is how it looks in an equation y = -2x When you use the formula to find the rate, it will look like this: How? : Pick 2 ordered pairs, then find the difference between the y-coordinates by the difference between the x-coordinates Try points ( , ) and ( , ) *************************************************************************************************************************** ___________ rate of change: as the input (x) increases or decreases, the output (y) stays the same. This is how it looks in a table: x y 0 5 3 5 9 5 This is how it looks in a graph Practice Rate of Change Temperature: Use the table at the right. It shows the outside air temperature at different times during one day. This is how it looks in an equation y=5 Name____________________________________ 1. Find the rate of temperature change in degrees per hour from 6am to 8am and from 4pm and 8pm. 2. Between which of these two time periods was the rate of change in temperature greater? 3. Make a graph of this data. 4. During which time period(s) was the rate of change in temperature positive? negative? 0 degrees per hour? How can you tell from your graph? Practice Rate of Change Temperature: Use the table at the right. It shows the outside air temperature at different times during one day. 1. Find the rate of temperature change in degrees per hour from 6am to 8am and from 4pm and 8pm. 2. Between which of these two time periods was the rate of change in temperature greater? 3. Make a graph of this data. 4. During which time period(s) was the rate of change in temperature positive? negative? 0 degrees per hour? How can you tell from your graph? Name____________________________________