Review of written homework mainly covering slope and box plots; as well as discovering what the y axis really means in an equation.
Finding a line in box plots can be done one of two ways either by algebraically solving, or using a calculator.
Slope Form - Y = mX + b where b is the y int.
USING A CALCULATOR TO FIND LINES - with data from homework
Use the STAT button and select edit. In column one fill in the X axis numbers in the homework example we would use 2, 4, 6, and 8. In the second column fill with the Y axis data. Once complete return to the STAT menu and go over to CALC there select LINEREG (line regression) and the calculator will place the equation together and reveal it. In order to see this equation in box plot go to the Y = menu and turn on the box plot function, then insert the equation and your plots will appear.
FINDING ALGEBRAICALLY - using data from Homework
First find the Slope
Change in Y / Change in X = M
M = 1.26-.726/4-2
M = .534/2 = .27 M = .27
Then use the equation Y- Y1 = M(X-X1)
The Y and X points come from the points chosen earlier.
Y - 1.26 = .27(X - 4) - this is point slope form with a slope of .27
We also discussed what the Y intercept means in an equation. For our specific homework the Y int. represented the delay time taken to start and stop the watch. This varies per equation and has to be interpreted given the data and situation. However the Y int. is the point at which a line crosses the Y axis making the plot (0,#).
Class #6 (wed. 8-27-08) We worked as a class with the math model that relates coronary heart disease (CHD) to cigarette smoking. The LinReg model predicted the US deaths due to CHD with an error of about 7%; we discussed the fact that the model has a negative y-intercept (not reasonable) and that this probably means that the model needs to level out as cigarette smoking levels near zero. We also mentioned other factors that the model does not take into account: diet, environmental factors, genetics, amount of exercise. This is typical of a model; it simplifies things in order to focus on key relationships, in this case the impact cigarette smoking has on CHD. We also read verbal descriptions of five relationships and sketched graphical representations. This provided practice with independent and dependent variable recognition, and it will serve as a lead in to using non-linear functions as math models.
Week 3, class 1. We started off discussing the accuracy of the predictions for the path of Hurricane Gustav and some of the variable quantities that they use in making these predictions (barometric pressure, wind velocity and direction, water temperature of the water the storm passes over, etc. We discussed the idea that we are doing similar things on a smaller scale: using functions to make predictions. We are getting ready to do some quadratic function modeling, so we are reviewing the algebra and graphs of quadratic functions. Today's class focused on starting with an equation and obtaining the y-intercept, x-intercept, vertex, axis of symmetry and the reflection point of the y-intercept across the axis of symmetry. We focused on vertex form and reviewed how to change an equation into vertex form. We also reviewed a linear modeling question in which we interpreted the meaning of the intercepts and the slope of a linear model. y = -3t + 48 Since t represented time (in sec) after a driver took her foot off the gas pedal and y represented the speed of the car (in mph), the slope represents the rate of change in the speed (in mph)for each second that elapses. So in our case the speed decreases 3 mph for every second. Note that the units are (mph per second)
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Aug 21 Notes Section C
Review of written homework mainly covering slope and box plots; as well as discovering what the y axis really means in an equation.
Finding a line in box plots can be done one of two ways either by algebraically solving, or using a calculator.
Slope Form - Y = mX + b where b is the y int.
USING A CALCULATOR TO FIND LINES - with data from homework
Use the STAT button and select edit. In column one fill in the X axis numbers in the homework example we would use 2, 4, 6, and 8. In the second column fill with the Y axis data. Once complete return to the STAT menu and go over to CALC there select LINEREG (line regression) and the calculator will place the equation together and reveal it. In order to see this equation in box plot go to the Y = menu and turn on the box plot function, then insert the equation and your plots will appear.
FINDING ALGEBRAICALLY - using data from Homework
First find the Slope
Change in Y / Change in X = M
M = 1.26-.726/4-2
M = .534/2 = .27
M = .27
Then use the equation Y- Y1 = M(X-X1)
The Y and X points come from the points chosen earlier.
Y - 1.26 = .27(X - 4) - this is point slope form with a slope of .27
We also discussed what the Y intercept means in an equation. For our specific homework the Y int. represented the delay time taken to start and stop the watch. This varies per equation and has to be interpreted given the data and situation. However the Y int. is the point at which a line crosses the Y axis making the plot (0,#).
Class #6 (wed. 8-27-08)
We worked as a class with the math model that relates coronary heart disease (CHD) to cigarette smoking.
The LinReg model predicted the US deaths due to CHD with an error of about 7%; we discussed the fact that the model has a negative y-intercept
(not reasonable) and that this probably means that the model needs to level out as cigarette smoking levels near zero. We also mentioned other factors that the model does not take into account: diet, environmental factors, genetics, amount of exercise. This is typical of a model; it simplifies things in order to focus on key relationships, in this case the impact cigarette smoking has on CHD.
We also read verbal descriptions of five relationships and sketched graphical representations. This provided practice with independent and dependent variable recognition,
and it will serve as a lead in to using non-linear functions as math models.
Week 3, class 1.
We started off discussing the accuracy of the predictions for the path of Hurricane Gustav and some of the variable quantities that they use in making these predictions (barometric pressure, wind velocity and direction, water temperature of the water the storm passes over, etc.
We discussed the idea that we are doing similar things on a smaller scale: using functions to make predictions.
We are getting ready to do some quadratic function modeling, so we are reviewing the algebra and graphs of quadratic functions.
Today's class focused on starting with an equation and obtaining the y-intercept, x-intercept, vertex, axis of symmetry and the reflection point of the y-intercept across the axis of symmetry. We focused on vertex form and reviewed how to change an equation into vertex form.
We also reviewed a linear modeling question in which we interpreted the meaning of the intercepts and the slope of a linear model. y = -3t + 48
Since t represented time (in sec) after a driver took her foot off the gas pedal and y represented the speed of the car (in mph), the slope represents the rate of change in the speed (in mph)for each second that elapses. So in our case the speed decreases 3 mph for every second. Note that the units are
(mph per second)
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