Graphing Linear Equations

If you are looking to graph a liner equation with the help of a calculator, all you need is know is a few things about the equation and being good at plotting points in a graph.

To graph a linear equation, let’s use the popular y intercept form (y=mx+b). This is also one of the easiest methods to graph linear equations. You don’t need the values to be whole numbers in the equation as you can see equations of all types. So, let’s look at graphing this linear equation below:

Y = 1/4x + 5

Let’s use the y intercept method, so y=mx+b, and ¼ is m here and b is 5. M is also known as the slope. The slope is also termed as the rise over run value and ¼ is the slope.

B is known as the y intercept where the line intersects with the y axis.

So, we have ¼ as the slope and 5 as the y intercept.

And in the equation, y=1/4x + 5, here y and x are the variables.

To graph a linear equation, you need two points:

(x1, y1) and (x2,y2) ,

When you draw a line between these 2 points and connect these, you have successfully graphed a linear equation.

Example 1: – Graph the equation x+2y=9

Here we need to find the x intercept and y intercept by making both x and y as 0.

When x=0, we get:

0+2y=9y=4.5

So, our first point is (0, 4.5)

When y=0, we get:

x+2(0) =9x=9

So, our second point is (9, 0).

So the two points are (0,4.5) and (9,0).

Now all you need is to plot these 2 points correctly in the graph. Below is a diagram of the points graphed on the coordinate plane.

coordinate plane

Example 2: Graph the linear equation y = 2x + 3

First, we need to find the x and y intercept.

When x = 0, y = 2(0) + 3 = 0 + 3 = 3

The first point is (0, 3)

When y = 0, we have the following:

0 = 2x+3
-3 = 2x
-3/2 = x

The second point is (-3/2, 0)

The two points are (-3/2, 0) and (0, 3)

Now all you need is to plot these 2 points correctly in the graph. Below is a diagram of the points graphed on the coordinate plane.

linear equation