We are able to find the equation of a line when we know its gradient and a point it passes through.
e.g. Let's say we want to find an equation of a line with a gradient 2, passing through the point (4, 5).
Start with a general equation of a straight line: y = mx + c
m represents the gradient, c represents the y-intercept (i.e. the point where the line crosses the y-axis).
We know the gradient, so we can replace m with 2.
This gives us: y = 2x + c
To work out the value of c, we need to substitute the coordinates of the point given to us into our equation.
The coordinates here are (4, 5) so we know that x = 4 and y = 5.
This means that:
5 = 2 × 4 + c
5 = 8 + c
5 - 8 = c
-3 = c
Now let's put everything together to get our final equation for this line: y = 2x - 3
It is also useful to know that parallel lines have the same gradient.
You can use this property of straight lines when the question does not specifically tell you what the gradient is.
In this activity, we will find the equations of straight lines when we are given, or can calculate, the line's gradient and a point it passes through.
You will also need to recognise and apply the similar properties of parallel lines.