Tips from the Pros

Day 5

1Daily Objective: Students will write an equation with given data points.

When given data points its about the same method as using a graph

We will use the data points (5,10) and (6,11)

You use the formula y=mx+b and first need to find the slope.

You will use the formula y2-y1 

                                         x2-x1

it will look like this: 11-10

                                 6-5

You subtract that to get 1. The slope is one.

Now that we have m in our formula we need to find b.

To find b we put our slope into our formula as well as one of the points.

it will look like this:

10=1(5)+b.

5x1=5. Now you have to subtract 5 to get b alone. You will subtract 5 from 10 too.

that gives you 5=b. 

Now you have the equation y=1x+5.

Heres a video also explaining it:

http://www.youtube.com/watch?v=GFM8NOe_XM4

Questions:

whats the equation of the points (1,1) and (2,2)?

Whats the equation of the points (3,3) and (4,4)?

Whats the equation of the points (5,5) and (6,6)?

Answers:

1.)

2.)

3,)

Day 4

Daily Objective: Students will graph linear inequalities

A Linear Inequality involves a linear expression in two variables by using any of the relational symbols such as <, >, ≤ or ≥

 Heres what it looks like:

    

First you will need a linear inequality. We will use y≥5x+1. 

So we will graph it out with the equation 5x+1. once we graph it we make a line of best fit because it is a positive line. If its negative it will look like this

It will have a dashed line.

Now that we have graph our equation with the line we will now have to shade. Because y is greater than our  equation, we will shade everything to the on the side of the line where the y axis is.

It is the same for negatives except a dashed line

Questions:

1.) graph the linear equality y> 6x+1

2.) graph the linear equality y<4x+1

3.) graph the linear equality y>8x+1

Answers:

1.)

                       2.)

                     3.)

Day 3

Daily Objective: Students will define the y intercept in math as well as translate it to a real world meaning.

The y intercept is where a straight line crosses the Y axis of a graph.

Heres a video explaining how it would be used in the real world

http://www.youtube.com/watch?v=Q62zjVbj3jc

Lets say we have the equation 3x+7 for the cost of the football. 7 is the y intercept. What it is saying is that before the football is sold in stores, it costed 7 dollars to make. So the real world meaning is that they needed 7 dollars to make the football.

Questions:

1.) What is the y intercept?

2.)How does a football have anything to do with a y intercept?

3.) Make another example of how the y intercept is used in real life.

Answers:

1.) the y intercept is the point when a line crosses the y axis.

2.) The y intercept shows what the football cost in the beginning.

3.) Lets say you have the equation 12x+100 for a basketball's cost. The 100 shows what the basketballs cost to make was.

Day 2

Daily Objective: Students will write linear equation of a line using data

The linear equation is an equation that makes a straight line when it is graphed.

Often written in the form: y = mx+b

A linear equation is in the form y=mx+b. So do find that equation we need a graph.

For this example we will use this graph:















Now that we have a graph we need to pick 2 points on the line of best fit. We will use (10,8) and (14,10). In the form y=mx+b, the m is the slope. To find slope we need to do y2 - y1.

                                                                                                                         x1 - x2

So with our points it would look like 10-8.

                                                          14-10

that will give us 2 or 1 .

                        4     2

So now we have in our linear equation: y=1/2x+b. to find the b in the equation we use one point. We will use (10,8). we plug it into our equation. 8 is the y and 10 is the x.

it looks like 8=1/2(10)+b. now you times 10 by 1/2 and get 5. Now you subtract the 5 from both sides and 8-5= 3. Now you have 3=b which is your b.

Now you have your linear equation which is y=1/2x+3.

Questions:

1.) Find the equation of  graph with the points (10,2) and (5,6).

2.) What does the m stand for is the linear equation form of y=mx+b?

3.) how do you find the b part in the linear equation y=mx+b?

Answers:

1.)

2.) The m stands for the slope

3.) To find the b you need the slope. you take an equation and put the y and the x where it is in the equation. than you times the slope by x and than either add or subtract to make whatever the answer is to be 0. than you add or subtract that to your y and there's your b part.

Day 1

     Daily Objective: Students will use the line of best fit to find equations of lines.

The line of best fit is a line on a graph showing the general direction that a group of points seem to be heading.

  To get the line of best fit you will need to have at lease two points. If you only have 2, than you connect them. If you have more than 2, you will need to find two points that are in the middle in the graph. Here is an Example:

As you can see this graph has a line that is through the middle of the graph. They have the same amount of points on both sides of the line. Which is two.

Heres a Youtube video explaining what a line of best fit is:

http://www.youtube.com/watch?v=RGg48FvWAWI

Questions

#1) Find the line of the best fit for the points (1,1) (2,5) (3,2) (-4,-3) (-1,-5)

#2) Find the line of best fit for the points (1,1) (2,2) (3,3) (-2,3) (-1,3) (-3,2)

#3) Find the line of best fit for the points (-1,4) (4,-1) (2,4) (-1,1)

Answers:

1.)

2.)

3.)