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Drawing a graph of a linear equation

Drawing a graph of a linear equation

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Summary

Drawing a graph of a linear equation

In a nutshell

The equation of a linear graph is y=mx+cy=mx+c. Given values of mm and cc​, this equation can be used to plot a straight line graph.


Reminder of y=mx+cy=mx+c

The gradient of a line is given by mm. It indicates the steepness of the line and can be calculated with:

m=change in ychange in xm=\frac{\text{change in }y}{\text{change in }x}​​


The yy-intercept is given by cc​. This is the point on the yy​-axis where the line crosses.


Using y=mx+cy=mx+c to draw the line

One way to draw a straight line graph is to figure out two points that the line passes, before joining up those points and extending the line beyond them. Follow this procedure:


​​PROCEDURE

1.
The easiest point to start with is the yy-intercept, given by cc, since you know this is on the yy-axis. Hence you have that the point (0,c)(0,c) is on the line. Mark this on the coordinate grid.​
2.
To find another point, simply pick an xx-value (other than zero, since this will just give you the point you already have) and insert it into the equation of the line to find the corresponding yy-coordinate.​
3.
Mark on this second point and join it up with the first point.



Example

A line has equation y=3x4y=3x-4. Find the coordinates of two points on the line. Hence draw the line given by the equation.​


Firstly, use the yy-intercept (x=0)(x=0)​ to find the first point: c=4c=-4 

Point 1: (0,4)\underline{(0,-4)}


Next, pick a non-zero xx-value. In this instance, x=1x=1. Insert this into the equation of the line:

y=3x4=3(1)4=34=1y=3x-4=3(1)-4=3-4=-1​​

Point 2: (1,1)\underline{(1, -1)}


Plot the two points found ((0,4)(0,-4) and (1,1)(1,-1)) then join them up, extending beyond those points.



Exceptions

Not all linear graphs have the equation y=mx+cy=mx+c. Vertical lines have equations of the form x=dx=d where dd is a constant. These lines have the same xx-coordinate all along the line, so are represented by a vertical line going through x=dx=d given a value of dd.


Horizontal lines technically do have the form y=mx+cy=mx+c but where m=0m=0. These are just horizontal lines that go through cc on the yy-axis.​


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FAQs - Frequently Asked Questions

What shape is a linear graph?

What is a linear equation?

How do you use an equation of a line to find a point on the line?

How do you plot a linear graph from the equation?

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