Are you confused about coordinate planes? Well, don't worry! We will show you how to plot points on a Cartesian plane, find coordinates of a specific point and draw linear relationships on a Cartesian plane.
The Cartesian Plane provides a method of representing pairs of numbers that are related, as coordinate points.
If we plot multiple points, we can represent general mathematical relationships such as linear equations.
|NSW Stage 4 NESA Syllabus|
|Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)|
|Plot linear relationships on the Cartesian plane, with and without the use of digital technologies (ACMNA193)|
Students should be confident with basic algebraic techniques such as substitution and have a basic understanding of linear relationships.
The cartesian plane is a grid which can be used to represent points.
Each point is a pair of numbers with an \( x \) and \(y number.
Eg. A [latex](2,5)\) means for a point \(A\), the \(x\) coordinate is \(2\) and the \(y\) coordinate is \(5\) :
Conversely, we can find the coordinates of a point B[/latex] on the plane:
So, we write \(B(1,3)\).
When we are given a linear relationship such as \( y = 5 + x \), we can represent this on a cartesian plane by determining which points the relation goes through and joining them to form a straight line.
To do this, first we create a table of values:
Then we can plot each point on the coordinate plane, and draw a line that goes through these points:
Any points that lie on the line (even those that aren’t points on the grid) are solutions to the linear relationship \( y=5+x \).
The line continues forever, so there are infinite solutions to this relation.
For example, we can see that the point \((5,10)\) lies on the line, and so when \( x=5 \), \(y=10\), we have \(10 = 5 + 5\).
We can also determine linear relationships based on lines on a cartesian plane.
For example, consider the following line:
Looking at the points marked on the line, we can construct the following table:
|\( x \)||0||1||2||3|
|\( y \)||3||5||7||9|
What is the equation represented by this line?
We know that when \( x = 0 \), \( y = 3 \); and the difference between successive \( y \) values is \( 2 \).
So, therefore our equation must be \( y = 3 + 2x \).
Now we have covered reading points from a graph, constructing a line on the cartesian plane by plotting values, and finding the equation that is represented by a given line on the coordinate axes.
2. Given \(y = 3x-x\), find 3 points on the line and hence plot the line.
3. Determine the linear relation governing the following line.
|\( x \)||0||1||2|
|\( y \)||3||6||9|
3) \( y = 2x – 3 \)
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