Finding rates of change from tables and graphs.

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Presentation transcript:

Finding rates of change from tables and graphs. WHAT YOU’LL LEARN: Finding rates of change from tables and graphs. AND WHY: To find rates of change in real-world situations, such as the rate of descent for a parachute or the cost of renting a computer.

Suppose you type 140 words in 4 minutes. What is your typing rate? RATES OF CHANGE Suppose you type 140 words in 4 minutes. What is your typing rate? 140 words 4 min 35 words 1 min = The number of words depends on the number of minutes you type. So, the number of words is the dependent variable.

RATES OF CHANGE $19.99 $3.99 5 yd 1 yd = 268.8 mi 22.4 mi 12 gal 1 gal Write each as a rate. You buy 5 yards of fabric for $19.95. You travel 268.8 mi on 12 gal of gasoline. $19.99 5 yd $3.99 1 yd = 268.8 mi 12 gal 22.4 mi 1 gal =

change in the dependent variable change in the independent variable = RATES OF CHANGE You use a rate of change to find the amount of one quantity per one unit of another, such as typing 35 words in 1 min. The RATE OF CHANGE allows you to see the relationship between two quantities that are changing. rate of change change in the dependent variable change in the independent variable =

dependent variable (RISE) independent variable (RUN) RATES OF CHANGE On a graph, you show the dependent variable on the vertical axis and the independent variable on the horizontal axis. change in the dependent variable (RISE) independent variable (RUN)

Rate of Change of a Linear Relationship rise run Rate of Change = The rate of change of a linear relationship is the steepness of the line. When a graph shows a straight line (with a constant rate of change), it represents a linear relationship

LINEAR FUNCTIONS 2 The rate of change is . 3 8 6 4 2 Is this relationship linear? Why? Find the Rate of Change: Graph 0 2 4 6 8 x y 8 6 4 2 2 units 3 units The rate of change is . 2 3

LINEAR FUNCTIONS From a table, you must find the difference in the dependent variables (y) and compare that to the difference in the independent variables (x). Table Change in y values Change in x values x y 0 1 3 3 6 5 9 7 3 2 3 2 3 2 2 units 3 units When tables show a constant rate of change, they represent a linear relationship

LINEAR FUNCTIONS Is this relationship linear? Why? Find the Rate of Change:

Find the rate of change for each situation. LINEAR FUNCTIONS Find the rate of change: Does this represent a linear function? Why? Price of Oregano Cost (dollars) Weight (ounces) 0 1 2 3 4 5 6 2 1 1 6 $1 buys 6 oz of oregano.

About 1 gal used for every 15 mi. LINEAR FUNCTIONS Find the rate of change: Does this represent a linear function? Why? A Tank of Gas 15 10 5 Fuel in Tank (gallons) 0 100 200 300 Miles Traveled 1 15 About 1 gal used for every 15 mi.

Find the rate of change for each situation. LINEAR FUNCTIONS Find the rate of change: Does this represent a linear function? Why? x y 1 -2 -5 -8 1 -3 YES 1 -3 1 -3

Find the rate of change for each situation. LINEAR FUNCTIONS Find the rate of change: Does this represent a linear function? Why? x y 1 4 8 9 2 1 NO 2 3 2 5

Find the rate of change for each situation. LINEAR FUNCTIONS Find the rate of change: Does this represent a linear function? Why? x y 0 3 6 9 12 1 3 YES 1 3 1 3

Find the rate of change for each situation. LINEAR FUNCTIONS Find the rate of change: Does this represent a linear function? Why? x y 1 3 3 7 4 9 7 15 2 4 YES 1 2 3 6 Rate of change is 2.