3.1 to 3.3

Hi. The stuff covered in 3.1 to 3.3 is pretty much all things we have already learned. The first concept covered is the Cartesian Cordinate system with a x-axis, a y-axis, and four quadrants pictured below.



The next thing covered is the distance formula . The distance between any two points (x₁, y₁) and (x₂, y₂) is



The distance formula can be proved drawing a right triangle between points and finding the length of the hypothenuse using the Pythagorean Theorem as shown below.



Next we learned about the Midpoint formula. The midpoint of the line segment from (x₁, y₁) to  (x₂, y₂) is

This can be proved because the x-cordinate of the midpoint is equal to the average of the x-cordinates of the endpoints. The same goes for the y-cordinate. That's pretty much everything in 3.1.

3.2 deals with the graphs of equations. We went over some basic terminology.
     Solution: And ordered pair that yeilds a true statement
     X-intercepts: The x-cordinates of the points where a graph intersects the x-axis
     Y-intercepts: The y-cordinates of the points where a graph intersects the y-axis
You can find the x-intercept of a function by substituting the y value with 0. You can find the y-intercept by substituting the x value with 0.

The next thing covered is graphs of circles. The standard equation of a circle with center (h,k) and radius r is

Keep in mind that circles are not a function because they don't pass the vertical line test. If you want to graph a circle on your graphing calculator (which only graphs functions) you can graph two semicircles. All you have to do is solve the equation for your circle for y, which will lead you to two answers (±). For y1 enter the positive value of the equation and for y2 enter the negative value.

3.3 goes over lines

The slope of a line is defined by the formula

If the line is parallel to the y-axis, then the slope is undefined. A line parallel to the x-axis has a slope of 0.

Another important equation is the Point-Slope Form. An equation for the line through point  (x₁, y₁) is 

y – y₁ = m(x – x₁)

The books also talks about standard form (ax+by=c) which Mr. Wilhelm said we don't have to know.

We also went over relationships between lines.

Two nonvertical lines are parallel if and only is they have the same slope and two lines with opposite reciprical slopes are perpendicular.

Well thats pretty much everything. Bye.

     -Corn Murphy