Chapter overview



Drawing a graph of a linear equation

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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:


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.​
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.​
Mark on this second point and join it up with the first point.


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:


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.


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.​

Frequently Asked Questions (FAQ)


  • Question: What shape is a linear graph?

    Answer: A linear graph is a straight line.

  • Question: What is a linear equation?

    Answer: y=mx+c is a form of the linear equation. It gives a straight line when plotted.

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

    Answer: Choose any x-coordinate and insert it into the equation of the line. This will give the y-coordinate. Hence you have the coordinates of a point on the line.

  • Question: How do you plot a linear graph from the equation?

    Answer: Use the equation to locate two points on the line. Join these points up and extend the line beyond them.



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