We can represent all the solutions to $x+y = 7$ by graphing the equation on a coordinate plane.

The graph is a line. All the points on the line are solutions to $x+y = 7$.

On a coordinate plane, the solution to $x+y \leq 7$ includes the line that represents $x+y=7$. If we plot a few other $(x,y)$ pairs that make the inequality true, such as $(4, \text-7)$ and $(\text-6,0)$, we see that these points fall on one side of the line. (In contrast, $(x,y)$ pairs that make the inequality false fall on the other side of the line.)

We can shade that region on one side of the line to indicate that all points in it are solutions.

On a coordinate plane, the solution does not include points on the line that represent $x+y=7$ (because those points are $x$ and $y$ pairs whose sum is 7).

To exclude points on that boundary line, we can use a dashed line. 

All points below that line are $(x,y)$ pairs that make $x+y<7$ true. The region on that side of the line can be shaded to show that it contains the solutions.