April 27, 2011

There are 3 types of lines:

1. Parallel lines - the slope for each line is the same.  There is no common solution.  "My son and I will never be the same age".  
2. 1 intersection - intersect at exactly one point.  The lines will never intersect again.  There is 1 common solution.  The point makes the equation for both lines true.  "My dog and I will eventually be at the same age because we age at different rates."
3. Infinite intersection lines - all intersecting points are common.  "My identical twin and I will always be the same age."

Solving Systems by Graphing:

The lines intersect at (4,10)
The solution to this system is x = 4, y = 10

Another system to solve: 

The lines intersect at (2,4)
Solution to this system is x = 2, y = 10

**Sometimes the systems are not in slope intercept form.  So, in that case you need get it there.**

Example:

• x + y = 8 and y = 3x
• x + y = 8 is not in slope intercept form.  Subtract x from both sides.  The equation then turns into: y = -x + 8.  This is now in slope intercept form.



The lines intersect (2,6)
The solution to this system is x = 2, y=6

We used a graphing calculator to solve these problems. We had to find the intersection
and in what quadrant.
#1 is (-1,2) Quadrant 3
#7 is (-1,3) Quadrant 2
#10 is (3,8) Quadrant 1
Free online Graphing Calculator
you can use the above link to solve these problems.

This is a problem we solved, but I used the online graphic calculator 

Another problem that we did.  I did this one on paper, using two different methods.
*The first putting both equations in slope intercept form and them using a graphing
calculator.
*The second, using a T table for each equation and looking for coordinates
that are identical

Write the equations in slope intercept form. 

(don't solve the systems)

April 13, 2011

Homework problems

Graph for this problem is below

This is the graph for the answer for problem #1.  y = 1x + 5

The graph for this problem is below.

This is the graph for y = -2x - 6

Free online graphing calculator - Thanks for sharing Julie!!

April 6, 2011 - Graphing

A Maths Dictionary for Kids

What is linearity?  The study of lines.

• Directionality
• Ordered Pairs
• Graph
• Equation

Linear

Coordinate Plane

Quadrants of Coordinate Planes

Ordered Pairs

Slopes

• Slope (or rate of change) - the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.  
• Slope = rise/run (rise over run)
• always treat slope in the simplest form

Types of Slopes:

Positive slope - rises left to right

Negative slope - goes down - left to right

Zero slope - never rises, never a change in y

Undefined slope - perfectly up and down line  - x never changes
Always in the form of x = 

Examples:

3/2 (think fraction)

4/3

-2/5

-3 or -3/1

Slope Triangle

The red line is the slope I am starting with.  The white lines are helping me determine the slope.

Up 3 over 3 = 3/3...or in simplest for 1/1

Up 2 over 3 = 2/3

Negative slope
Down 4 over 5 = -4/5

The slope is 3/4.  The red and blue lines represent the slope triangle.

Formula for the slope intercept of a line  

• y = mx + b 
• the m represents the slope - how fast that line is changing
• y and x are the variables
• b = y intercept
• intercept is when a line crosses the axis. The y intercept is where the line crosses the y axis

Drawing Slopes

If your slope has a negative like - 3/5....assume that the numerator (in this case the 3)
is the negative #.  You could assume that the 5 is negative number....if you
do, you will get the same slope.

Stories to graphs

Using Coordinates to determine slope