What shape is a linear graph?

A linear graph is a straight line.

What is a linear equation?

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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Chapter overview

Learning goals

Maths

Drawing a graph of a linear equation

Your lesson progress

Summary

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Drawing a graph of a linear equation

In a nutshell

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.

Drawing a graph of a linear equation

In a nutshell

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.

Maths; Straight line graphs; KS3 Year 7; Drawing a graph of a linear equation

Exceptions

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.

Frequently Asked Questions (FAQ)

FAQs

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.

Theory

Exercises

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Drawing a graph of a linear equation

Drawing a graph of a linear equation

In a nutshell

Reminder of y=mx+cy=mx+cy=mx+c

Using y=mx+cy=mx+cy=mx+c to draw the line

​​PROCEDURE

Example

Exceptions

Drawing a graph of a linear equation

In a nutshell

Reminder of y=mx+cy=mx+cy=mx+c

Using y=mx+cy=mx+cy=mx+c to draw the line

​​PROCEDURE

Example

Exceptions

Now you’ve read the summary, have a go at the exercises!

Reminder of $y=mx+c$

Using $y=mx+c$ to draw the line

PROCEDURE

Reminder of $y=mx+c$

Using $y=mx+c$ to draw the line

PROCEDURE