Graphing Linear Equations: When Y = 2/3 XI am trying to figure out how this graph made sense if the coordinates never lined up properly. My numbers were for x,y (0,0) (3,2) (6,3) and somehow I got it right on the practice test even though I guessed on the graph part. I am writing to you without the completed graph because the system would not allow me to post pictures or images.Can I have some feedback with a graph on this please?Shawn Williams
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Graphing Linear Equations: When Y = 2/3 X
I am trying to figure out how this graph made sense if the coordinates never lined up properly. My numbers were for x,y (0,0) (3,2) (6,3) and somehow I got it right on the practice test even though I guessed on the graph part. I am writing to you without the completed graph because the system would not allow me to post pictures or images.
Can I have some feedback with a graph on this please?
Shawn Williams
For a line to pass through three given points, the points need to be collinear.
To check if points are collinear, the slopes of the lines joining them may be checked.
Let A(0,0), B(3,2), C(6,3)
The slopes are given by:
Since the slopes are not equal, the points are not collinear and no line shall pass through all the three points.
So the line y=2/3 x doesn\'t pass through all the three points.
To check the points lying on the given equation of the line, plugging x=0,3,6 in the equation:
Hence the points lying on the graph of the equation y=2/3 x are (0,0),(3,2) and (6,4)
It can also be seen in the graph.
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