 # Linear Equations

Note by , created almost 6 years ago

## This note explains what linear equations are and how they can be used 285 8 0  Created by rory.examtime almost 6 years ago
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### Page 1

A linear equation is an algebraic equation with two variables (x &amp; y) which refers to a line in the co-ordinate plane.

There are two common forms of linear equations:

﻿﻿1.  y = mx + c

﻿- m and c are constants- m is equal to the slope of the line.

﻿﻿2. ax + by + c = 0

﻿- a, b and c are constants

If we know the equation of a line, we can plot it on the co-ordinate plane.

This is done by subbing a value for x (usually 0) to find a corresponding y-value, and vice versa.

x represents the horizontal co-ordinate

y represents the vertical co-ordinate

E.g :﻿y = 4x + 7     ﻿

Let x = 0

﻿y = 7

=&gt; (0, 7) is on the line

Then, let y = 0

0 = 4x + 7

﻿4x = -7

﻿x = -4/7

=&gt; (-4/7, 0) is also on the line.

Now that we have two points on the line, we can plot it by drawing a straight line which passes through both.

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