A graph is a visual picture of data that helps you see relationships. In Math or Science you may need to graph data on a Cartesian graph that includes variables. The acronym DRY MIX is a very easy way to help remember how to set up the graph properly.Rene Descartes in the 1600’s devised a way to make visual pictures of algebra equations. He was able to blend algebra and geometry.
Let’s look at the equation,
x = 3y – 2
Create a quick T-table so we can graph it
The x will be your independent variable, and the y will be your dependent variable because it depends on the value of x.
Use DRY MIX in order to help me set up the graph properly.
DRY stands for
D = Dependent variable
R = Responding Variable
Y = y axis
MIX stands for
M = Manipulated variable
I = Independent variable
X = x axis
The y axis runs up and down or vertical, and contains the dependent variable.
The x axis runs left and right, and contains the independent variable.
Hi Welcome to MooMooMath Today we are going to look at a coordinate plane. Now what is a coordinate plane? Remember a plane has two directions an X and a Y direction and it has a flat surface. So we are going to look at how to graph points on the coordinate plane. Now the horizontal plane is the X axis and the vertical axis is the Y axis. An easy way to remember this is to think about the long stem on the Y so the Y goes up and down if you forget. Here is the point (0, 0) and that is the origin and from here we will count left negative and right positive. Now let’s look at the Y axis. Anything that is going up is positive value and anything going down will be negative value. We write our values on the Cartesian coordinate plane as two variables. X is always the first direction and Y is always the second direction. So we always move left to right first and then up and down. So let’s try the point 4, 2 and they are both positive. We would count over 4 in the X direction and then up 2 in the positive Y direction. Let’s plot the point negative 3 positive 3 We now have a negative X direction which means we will start to the left and count 3 to the left for the X axis and up 2 for the Y axis and that becomes negative 3 positive 2. So now let’s talk about signs. If you are here in quadrant one you will have signs that are positive, positive. If you have a negative value for X and a positive value for Y you will be in quadrant II If you are going negative and negative this would put you in quadrant III an example would be negative 3 negative 1. The last option quadrant IV has a positive X and a negative Y so an example of a point in this quadrant is positive 2 and negative 3 so that is how the Cartesian coordinate plane is set up. Let’s look at an overview. We have the four quadrants I,II,III,and IV and they go in counter clockwise motion. The signs are ++ for quadrant I, negative. Positive for quadrant II, negative, negative for quadrant III. And positive, negative, for quadrant IV If you land on an axis like if you land on a Y axis your X value is zero and your Y value is wherever you are on that axis. Now it is reversed if you land on the X axis. You get a value of zero for Y and the X value is wherever you land on the X axis. So there you go that is the Cartesian coordinate plane and how it is set up.
Summary of the parts of the coordinate plane
Horizontal axis is labeled with the letter x
In a Cartesian coordinate system the vertical axis is labeled with the letter y
Ordered pairs of numbers are used to describe points on the coordinate plane. (x,y)
It is divided into four quadrants I,II,III,IV
x-coordinate is named the absissa
y-coordinate is named the ordinate
The origin is the intersection of the x and y axis. (0,0)
A Cartesian graph, also known as a Cartesian coordinate plane or system, can be used to describe the location of a point.
A Cartesian coordinate system is created by drawing a horizontal number line, called the x-axis, and a vertical number line called the y-axis.
The origin is the point where the horizontal ( x) and vertical (y) axis intersect. Ordered pairs of numbers called coordinates are used to locate a point on the coordinate plane.
The horizontal distance from the origin is the first number in an ordered pair, and the vertical axis is the second number. (x, y)
For example, the ordered pair (2, 4) would mean the point is 2 units to the right of the origin, and 4 units above the origin.
As numbers increase on the x-axis the point will move to the right, and on the y-axis, as numbers increase the location moves upward.
The Cartesian graphing system is also divided into four quadrants.
The quadrants are created from the intersection of the x and y-axis.
The upper right quadrant is labeled quadrant I and all points in this quadrant have positive x and y values.
If you move in a clock wise manner the next quadrant is II, and points in this quadrant have positive x values and negative y values.
Quadrant three has all negative values, and quadrant IV has negative x values and positive y values. The ordered pair (4,-2) would be found in quadrant II, four places to the right of the y-axis, and two places below the x-axis.