The relationship between f(x)=-2x+3

Question

The relationship between f(x)=-2x+3,

and g(x)=-2x-3

Answer 1

I like Daniel's explanation. I would only add that the lines are parallel.

Answer 2

f(x) and g(x) have the same gradient/slope of -2, but they have different y-intercepts: f(x) has a y-intercept of 3, and g(x) has a y-intercept of -3. The y-intercepts are found by subbing in x = 0 into both equations, f(0) = 3 and g(0) = -3.

So, f(x) is the same line as g(x), but shifted up six units along the y-axis, or alternatively, g(x) is the same line as f(x), but shifted six units down along the y-axis.

You could also describe it mathematically, f(x) = g(x)+6 or g(x) = f(x)-6.