Any two straight lines with differing gradients will always meet at one point. This is because their different steepness makes the lines closer together at some point.

Any two straight lines with same gradient and different y-intercept (or x-intercept) will never meet. This is because they are a distance away from each other at the y-axis, and due to the gradients being the same, this distance never changes.

Any two straight lines with identical equations in the base form y = mx + c will forever meet along the line. This is because their distance between them is always zero.

Equations like x + y = 4 and 2x + 2y = 8 are identical because the second form reduces to the first form exactly, whereas 2x + 2y = 16 is another line altogether and will never meet any of the above lines and other lines such as y = 5x + 3 will meet all of the lines above at exactly one point.