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

Reminder of $y=mx+c$

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

$m=\frac{\text{change in }y}{\text{change in }x}$

The $y$-intercept is given by $c$. This is the point on the $y$-axis where the line crosses.

Using $y=mx+c$ 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 $y$-intercept, given by $c$, since you know this is on the $y$-axis. Hence you have that the point $(0,c)$ is on the line. Mark this on the coordinate grid.

2.

To find another point, simply pick an $x$-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 $y$-coordinate.

3.

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

Example

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

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

Point 1: $\underline{(0,-4)}$

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

$y=3x-4=3(1)-4=3-4=-1$

Point 2: $\underline{(1, -1)}$

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

Exceptions

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

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

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

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

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.

How do you plot a linear graph from the equation?

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

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