How do you write the equation of a line parallel to y = x + 5?

To write the equation of a line parallel to \( y = x + 5 \), use the same gradient but a different y-intercept.

In more detail, the equation of a line in the form \( y = mx + c \) is called the slope-intercept form, where \( m \) represents the gradient (or slope) and \( c \) represents the y-intercept. For the given line \( y = x + 5 \), the gradient \( m \) is 1, and the y-intercept \( c \) is 5.

When two lines are parallel, they have the same gradient. Therefore, any line parallel to \( y = x + 5 \) will also have a gradient of 1. The only thing that will change is the y-intercept \( c \). This means the equation of any line parallel to \( y = x + 5 \) will be in the form \( y = x + c \), where \( c \) can be any real number.

For example, if you choose \( c = 3 \), the equation of the parallel line would be \( y = x + 3 \). If you choose \( c = -2 \), the equation would be \( y = x - 2 \). Essentially, you can pick any value for \( c \) to get a different parallel line.

So, to summarise, to write the equation of a line parallel to \( y = x + 5 \), keep the gradient the same (which is 1) and change the y-intercept to any other value.