697. Where are the points $(x, y)$ for which $y=2 x+1$?
$\triangleright$ To get such a point, you can first take a point $(x, y)$ where $y=2x$, and then increase $y$ by 1. In other words, you need to take the line $y=2x$ and then move all its points up by exactly 1, meaning the entire construction on the grid paper is simply shifted up by one cell. $\triangleleft$

In general:

Points $(x, y)$ that satisfy the equation $y=kx+b$ form a line. This line is parallel to the line $y=kx$ and intersects the y-axis at the point $(0, b)$ (when $x=0$, the equation gives $y=b$). Thus, any non-vertical line can be defined in this way.