MATH 101 Lecture #3 - Graphs
Hello, ignorant kids students. Just sit down quickly and hand in your problem sets, etc. etc. *is a bit nervous due to current events of a certain teacher coming into sbg ((Only super hacker students can comment on this k?))*
I guess I was a bit harsh on you last week (Pffff) by giving you a problem with imaginary numbers. But to the smarter students, I'm glad it was very easy to handle. Har har. Anyway, we'll be learning more about the visual aspects of various equations in the Cartesian plane.
((FYI THE x2 EXPRESSIONS ARE ALL X^2. They look like superscript to me so I didnt bother writing the carots. Sorry!!!!))
In mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point. To define the coordinates, two perpendicular directed lines (the x-axis, and the y-axis), are specified, as well as the unit length, which is marked off on the two axes (see Figure 1). Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimensions.
FIG 1
And you can translate most equations into this plane, like the few of the questions you had on the problem set. Anyway more on coordinates... *starts to furiously write*
A Cartesian coordinate system in two dimensions is commonly defined by two axes, at right angles to each other, forming a plane (an xy-plane). The horizontal axis is normally labeled x, and the vertical axis is normally labeled y. In a three dimensional coordinate system, another axis, normally labeled z, is added, providing a third dimension of space measurement. The axes are commonly defined as mutually orthogonal to each other (each at a right angle to the other).
The point of intersection, where the axes meet, is called the origin normally labeled O. The x and y axes define a plane that is referred to as the xy plane. Given each axis, choose a unit length, and mark off each unit along the axis, forming a grid. To specify a particular point on a two dimensional coordinate system, indicate the x unit first (abscissa), followed by the y unit (ordinate) in the form (x,y), an ordered pair.
The choice of letters comes from a convention, to use the latter part of the alphabet to indicate unknown values. In contrast, the first part of the alphabet was used to designate known values.
The intersection of the two axes creates four regions, called quadrants, indicated by the Roman numerals: Quadrant I (+,+) ;
Quadrant II (−,+); Quadrant III (−,−) ; and Quadrant IV (+,−). *marks them on the diagram Fig. 1*
Conventionally, the quadrants are labeled counter-clockwise starting from the upper right ("northeast") quadrant. In the first quadrant, both coordinates are positive, in the second quadrant x-coordinates are negative and y-coordinates positive, in the third quadrant both coordinates are negative and in the fourth quadrant, x-coordinates are positive and y-coordinates negative (see table below.)
Anyway... the most basic way to draw linear or any graph is to plug in random values of x and y and then map them accordingly on the plane...which, if you do every single pt of x, can produce the graph.... but usually people make do with a few points and then draw a line that best fits them.
Here are a few equations to graph/draw. *tosses a pile of graph papers to the students* NO RANDOM DOODLES ON MY GRAPH PAPER ALRIGHT? D:< *waves his yardstick threateningly*
Oh, and your first problem set/homework grades are up. Those who got below a C (aka C+'s is above cutline)...please see me OFFICE CLEANING TIEM!
((Either a chat or tegaki thread is good~))
Jeff : D+
Ganon: F
Bulbasaur: B
Amy Rose: B+
Goombella: A -
DinkToon Link: D
Guy: B+
Ninten: A -
Panther: B
Goombario: B-
Kirby: D-
Roy: B+
Green: D -
Totodile: B
Lucas: B+
Pit: A -
I guess I was a bit harsh on you last week (Pffff) by giving you a problem with imaginary numbers. But to the smarter students, I'm glad it was very easy to handle. Har har. Anyway, we'll be learning more about the visual aspects of various equations in the Cartesian plane.
((FYI THE x2 EXPRESSIONS ARE ALL X^2. They look like superscript to me so I didnt bother writing the carots. Sorry!!!!))
In mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point. To define the coordinates, two perpendicular directed lines (the x-axis, and the y-axis), are specified, as well as the unit length, which is marked off on the two axes (see Figure 1). Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimensions.
FIG 1
And you can translate most equations into this plane, like the few of the questions you had on the problem set. Anyway more on coordinates... *starts to furiously write*
A Cartesian coordinate system in two dimensions is commonly defined by two axes, at right angles to each other, forming a plane (an xy-plane). The horizontal axis is normally labeled x, and the vertical axis is normally labeled y. In a three dimensional coordinate system, another axis, normally labeled z, is added, providing a third dimension of space measurement. The axes are commonly defined as mutually orthogonal to each other (each at a right angle to the other).
The point of intersection, where the axes meet, is called the origin normally labeled O. The x and y axes define a plane that is referred to as the xy plane. Given each axis, choose a unit length, and mark off each unit along the axis, forming a grid. To specify a particular point on a two dimensional coordinate system, indicate the x unit first (abscissa), followed by the y unit (ordinate) in the form (x,y), an ordered pair.
The choice of letters comes from a convention, to use the latter part of the alphabet to indicate unknown values. In contrast, the first part of the alphabet was used to designate known values.
The intersection of the two axes creates four regions, called quadrants, indicated by the Roman numerals: Quadrant I (+,+) ;
Quadrant II (−,+); Quadrant III (−,−) ; and Quadrant IV (+,−). *marks them on the diagram Fig. 1*
Conventionally, the quadrants are labeled counter-clockwise starting from the upper right ("northeast") quadrant. In the first quadrant, both coordinates are positive, in the second quadrant x-coordinates are negative and y-coordinates positive, in the third quadrant both coordinates are negative and in the fourth quadrant, x-coordinates are positive and y-coordinates negative (see table below.)
Anyway... the most basic way to draw linear or any graph is to plug in random values of x and y and then map them accordingly on the plane...which, if you do every single pt of x, can produce the graph.... but usually people make do with a few points and then draw a line that best fits them.
Here are a few equations to graph/draw. *tosses a pile of graph papers to the students* NO RANDOM DOODLES ON MY GRAPH PAPER ALRIGHT? D:< *waves his yardstick threateningly*
Oh, and your first problem set/homework grades are up. Those who got below a C (aka C+'s is above cutline)...please see me OFFICE CLEANING TIEM!
((Either a chat or tegaki thread is good~))
Jeff : D+
Ganon: F
Bulbasaur: B
Amy Rose: B+
Goombella: A -
DinkToon Link: D
Guy: B+
Ninten: A -
Panther: B
Goombario: B-
Kirby: D-
Roy: B+
Green: D -
Totodile: B
Lucas: B+
Pit: A -