What do you know about the gradients of two parallel lines?

By definition, two straight lines are parallel if they have the same gradient. Using the standard form of a straight line y=mx+b, m represents the gradient. Gradient refers to the slope or steepness of a line or a curve at a given point; the higher the gradient, the steeper the line or tangent to the curve.

Example Question: Find the equation of the line that is parallel to y = 3x - 12 and passes through the point (0,3).

First, identify the gradient of the line y = 3x - 12 : m = 3

We are told the line we are asked to find the equation of is parallel to y = 3x - 12. Therefore, it must also have a gradient of 3, and have the form y = 3x + b.

How are we going to find b?

We are given a point of the line we are trying to find, namely (0,3). So we can substitute in these values for x and y into our standard form equation to obtain 3 = 3(0) + b.

Now we can use this to solve for b:

3 = 3(0) + b

b = 3

Therefore:

The equation of the parallel line passing through point (0,3) is y = 3x + 3.