PCH Ch 3.1 & 3.2

PCH Ch 3.1 & 3.2

Linear Functions & Linear Models: Have your graphing calculator ready. So first a few questions we think you already know the answers to.

Multiple Choice

The form of this linear equation is called..?

$$f\left(x\right)=mx+b$$  

• slope-interpole

• point-slope

• standard

• slope-intercept

Multiple Choice

The form of this equation of a line is called...?

$$y-y_1=m\left(x-x_1\right)$$  

• slope-corrdinate 

• point-slope

• standard

• slope-intercept

Multiple Choice

The form of this equation of a line is called

$$f\left(x\right)=ax^2+bx+c$$  

• slope-coordinate

• point-slope

• slope-intercept

• standard

Multiple Choice

For what values of x is this line increasing?

$$y=2x-7$$  

• this line is never increasing

• this line is always increasing

• just from 0 to -7

• doodlebug!

Multiple Choice

For what values of x is this line increasing?

$$f\left(x\right)=-32x-45$$  

• all values of x

• only at x = -45

• just odd values of x

• it's never increasing

​Slope of a line

​

The following list of ordered pairs would create a linear function

How would we know? If you take the difference from any adjacent pairs of values you would get 3 over 4.

Multiple Choice

Does this data represent a linear or nonlinear function?

• Yes, it's linear

• no, it's nonlinear

Multiple Choice

Given this information does this data represent a linear or nonlinear function?

• yes, it's linear

• no, it's nonlinear

Get your calculators out or get a yellow school bus one.  Turn it on.  

Let's start here

• push the enter key on the bottom right now find the STAT key next to the left arrow key and push it

• you will see EDIT and right under that you will see Edit so just push enter

• you will now see lists at the top of your calculator, it will look something like this but with no data ------------->

You will be typing in this list

• under L1 type in the weights. You will need to type the number then hit enter or arrow down

• When done use arrow keys to get UNDER L2 and type in the list for number of Raisins

• make sure you have the same number of values with each list.

• When done press the (blue) 2nd key and mode. the screen will go back to main screen. Data is still there!

Now....we need to turn on our STAT PLOT

press the (blue) second key and on the top row of keys press the narrow white y=

sorry this one is blurry but your window should look like this...

• if so push enter!

Your window should look something like this but we need to turn ours on

• you should see a blinking black square on the word ON. so push enter. Your black square should have moved off the word OFF and onto the word ON

• Now push the narrow white graph key and you see.....

You see NOTHING!

HA!

Do this so you will see something like this --->

• push the slender white "window" key and type 41 for Xmin and 44 for Xmax. use your arrow keys and go to Ymin and type 80 and Ymax and type 100

• then push the narrow white graph key

• TADA! You should see some squares, if you have a color enhanced TI calc they will be blue

• We will now have the calculator place a line of best fit!

Push the STAT key

• use arrow keys to slide over to CALC

• push the number 4

• you will see this screen

• 
  

Here comes the tricky part

Now you should see some numbers. y=ax+b

• a=11.44927

• b=-399.12318

• NOW push the narrow white graph key

• now push the narrow white y=

• so you should see a line on your scatter plot and you should see the equation in your y= list.

• so clearly a is the slope and b is the y intercept.

​

If you ever want to get back to the graph just push the narrow white graph key

• Your calculutor has done a scatter plot for you! Yes!

• It's place a line of best fit that we can all share and discuss the same outcome! Yes!

• You can also use your generated equation, called regression line,  for the line of best fit to get future information.

Push the alpha (green) button and then narrow white trace button and hit enter

This last thing you did was you used your line of best OR now called the linear regression line to determine the number of raisins if the weight of the box was 80 grams. Try this one....

Poll

How helpful was this activity?

• Super Amazing and I will watch it again

• Kinda cool

• meh

• I already knew how to do this.