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For example, \(\text{y = 2x + 1}\) and \(\text{y = 2x - 2}\) will be parallel because they both have a gradient of 2.

We want to determine if the lines \(\text{y = 4x + 5}\) and \(\text{2y - 8x = 6}\) are parallel.

The line \(\text{y = 4x + 5}\) is already in the form \(\text{y = mx + c}\) so we know it has a gradient of 4.

We will need to rearrange \(\text{2y - 8x = 6}\) into the same form to see if they are parallel.

\(\text{2y - 8x = 6}\)

Adding \(\text{8x}\) to both sides gives us \(\text{2y = 8x + 6}\).

But we need our equation to start with y on its own so we need to divide all the terms by 2, which gives us \(\text{y = 4x + 3}\).

This is now in the form \(\text{y = mx + c}\), so we can see that it also has a gradient of 4. Therefore, the lines are parallel.