Sections 3.1-3.3

Sections 3.1-3.3 Rectangular Coordinate Systems, Graphs of Equations and Lines

3.1

Section 3.1 deals with several important ideas. One of these important ideas is the distance formula. the distance formula is

this can be used to find the distance between any two points.

ex.

Another important formula is the midpoint formula. The midpoint formula is used to find the midpoint of a line.

ex.

3.2

Section 3.2 discusses graphs of equations. One way to create a graph is by plotting points.

ex.

Finding x and y intercepts.

y=x+4

set y=0 to find x intercept and x=0 to find the y intercept.

0=x+4

x=-4

x intercept is (-4,0)

y=0+4

y=4

y intercept is (0,4)

equation of a circle

the equation for a circle is (x-h)^2 + (y-c)^2=r^2 where (h,k) is the center of the circle and r is the radius.

how to find the center and radius of a circle.

in order to find the center and radius of a circle you must complete the square.

ex.

x^2+y^2- 4x + 6y=3

to find the center and radius you have to complete the square

(x^2 + 4x + _)+ (y^2 + 6y +_)=3+_+_

add (4/2)^2 and (6/2)^2. Don't forget to add to the other side

Then just simplify and you get

(x-2)^2 + (y+3)^2 =16

3.3

The line is a very important part of all math and should be understood thuroughly.

The slope of a line and being able to find it is also very important.

To find the slope you use the equation

ex.

This brings us to our next equation which is slope intercept form. This is expressed as

y=mx=b

where m stands for slope and b stands for the y intercept.

How to find equations for vedrticle or horizontal lines.

Find a line parallel to the x axis and a line parallel to the y axis that passes through the point (-5,6)

for the one parallel to the x axis the equation is x=-5

and for the one that is parallel to the y axis y=6

How to find the equation of a line that is parallel to a given line

ex.

6x+3y=4

3y=-6x+4

y=-2x+3

We have now found the slope , which is nessicary in order to find a parallel line.

Now plug in the other points, and the known slope into point slope form.

y+7=-2x+10

y=-2x+3

For finding a perpendicular line just do the same thing except take the opposit reciprical for the slope. For example in this case the slope in the second equation would be 1/2.

Matthew Silbergleit