What is the equation of a line parallel to y = 4x + 1?

The equation of a line parallel to y = 4x + 1 is y = 4x + c, where c is any constant.

To understand why, let's first look at the equation y = 4x + 1. This is in the form y = mx + c, where m is the gradient (or slope) of the line, and c is the y-intercept. In this case, the gradient m is 4, and the y-intercept is 1.

When two lines are parallel, they have the same gradient. This means that any line parallel to y = 4x + 1 must also have a gradient of 4. The only thing that can change is the y-intercept, which is represented by the constant c in the equation y = 4x + c.

For example, y = 4x + 3 and y = 4x - 2 are both parallel to y = 4x + 1 because they all have the same gradient of 4. The y-intercept changes, but the lines will never intersect because their gradients are identical.

So, to write the equation of a line parallel to y = 4x + 1, you simply keep the gradient the same (4) and change the y-intercept to any other value. This gives you the general form y = 4x + c, where c can be any constant.