What is the equation of a line parallel to y = -3x + 4?

The equation of a line parallel to y = -3x + 4 is y = -3x + c.

To understand why, let's first look at the equation y = -3x + 4. This is in the form y = mx + c, where m is the gradient (or slope) and c is the y-intercept. For the given line, the gradient m is -3.

When two lines are parallel, they have the same gradient. This means that any line parallel to y = -3x + 4 will also have a gradient of -3. The only thing that changes is the y-intercept, which is represented by c in the equation y = -3x + c.

For example, if we choose c = 2, the equation of the parallel line would be y = -3x + 2. If we choose c = -5, the equation would be y = -3x - 5. The value of c can be any real number, and it determines where the line crosses the y-axis.

So, to summarise, the key point is that the gradient must remain the same for the lines to be parallel. The y-intercept can vary, giving us a family of parallel lines all with the form y = -3x + c.