X y 10 20 30 40 50 x y 01 02 03 04 05. Review of definition: A function is a relation for which there is exactly one value of the dependent variable for.

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Presentation transcript:

X y x y

Review of definition: A function is a relation for which there is exactly one value of the dependent variable for each value of the independent variable.

The position of a speedometer needle depends on how fast the car is going.

The distance you travel depends on how long you have traveling (assume an average speed)

How badly your thumb hurts is a function of how hard you hit it with a hammer.

 The number of chirps a snowy tree cricket is a function of temperature.  (count the number of chirps in 13 seconds and add 40, this is the temp in Fahrenheit)   (mute at 2:00 – 2:05)

Your age and your height are related to one another.

Given (4,8) and (-2, 5) Find the equation in point-slope form and also in slope-intercept form, then graph the equation

Y = ½ x + 6

Given (-1,4) and (5, -14) Find the linear equation in point-slope form and slope intercept form and then graph the equation

Y=-3x+1

As you drive home from the football game, the number of miles you are away from home depends on the number of minutes you have been driving. (sketch a rough linear function of this relationship) Create variables for each element in the function. Label your axis.

Assume that the distance varies linearly with time. Suppose you are 11 miles away from home when you have been driving for 10 minutes, and 8 miles from home when you have been driving for 15 minutes. Find the equation to model this situation.

Solution: d = -3/5(t) + 17 a. What is your distance from home after 20 minutes? After 30 minutes? b. When are you 7 miles from home? c. What does y axis intercept represent? d. What does the x axis intercept represent? e. What are the units of slope? What does this represent?

Solution: d = -3/5(t) + 17 a. What is your distance from home after 20 minutes? 5 m After 30 minutes? -1 km b. When are you 7 miles from home? 50/3 or 16 2/3 min c. What does y axis intercept represent? Time = 0 distance = 17 miles from home is the stadium d. What does the x axis intercept represent? t = 28 1/3 (time you reach home) e. What are the units of slope? What does this represent? Miles/min (speed of travel or average velocity