How do you solve 3x plus y equals 7?

This is the equation of a line. There are an infinite number of solutions. All of the solutions are ordered pairs, (x,y) which represent points on that line.

For example take x=0 and y=7 so (0,7) is on the line.

Now take y=0 and x=7/3 is on the line. So the point (7/3,0) is on the lines.

Those two points are intercepts. If you graph them, you can connect them and you have a graph of the line.