The Number Line
First, let’s look at something familiar, the number line. On this line are all the numbers we know, 0, 1, 2, -1, π.
We can use our operators (+, – , x, ÷) to move along this line.
Check out our Algebra Resource for how to use these operators on variables.
The Four Quadrants
If we look at our number plane, we can see that it’s split up into four sections, which we call quadrants.
Graphing Equations – Constructing a Table of Values
In this section, we’ll look at the drawing some basic algebraic equations.
We’ll start with an easy example, y=x.
The first thing to do with these equations is to draw up a table of values. We start with some basic values of x (-2,-1,0,1,2,3) and see what values we get for y.
Each column gives us a pair of coordinates, ie (-2,-2), (-1,-1) etc. So, all that’s left to do is join the dots and we get a line.
Let’s try a trickier example, y=2x+1.
“I’ll do Algebra, I’ll do Trig, but Graphing is where I draw the line”
Distance and Midpoint
In this section we’ll be looking at some more geometric features of graphing, such as distance and midpoint.
In the next few sections, we’ll look at two key concepts to graphing, gradient and intercepts.
Firstly, gradient is the slope of a graph and you’ll commonly hear it as RISE/RUN, where RISE is the change in y and RUN is the change in x.
To find the gradient (which we call m), we need to know two points on the graph (x1,y1), and (x2,y2).
The formula to find the gradient is shown below.
For example, if we have two points, (-1,-3) and (2,3), we can calculate the gradient.
However, you may find it is sometimes difficult to find the Gradient-Intercept form of a line, especially when you don’t know the y-intercept!
But don’t worry, we have another tool in our graphing toolbox, and that’s the Point-Gradient formula.
For this formula, we need to only know a point on the line (x1,y1) and the gradient (m). Then we simply substitute into the formula.
For example, if we have a line which passes through (1,4) with gradient 2, we find a unique equation of a line.
Graphing the Parabola
Up until now, we’ve been looking at graphs that are straight lines. However, straight lines only make up a small number of graphs.
In this section, we’ll be tackling the famous parabola.
In the Algebra Learning Resouce, we learnt about quadratics. Just as straight lines are defined by the equation y=mx+b, parabolas are defined by quadratics, y=ax2+bx+c.
Let’s look at the standard parabola, y=x2. Our first step should always be to construct a table of values.
Variations in the Parabola
Just as there are variations in straight lines, there are also variations in parabolas.
When in doubt with how a quadratic is shifted or changed, just plug in a table of values!
Still Struggling with Graphing?
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