A course on mathematical knowledge for teaching might consider conditions under
which intersection points have integral coordinates. Teachers would learn that
the coordinates of the intersection point involve differences in the intercepts and
differences in the slopes, and that a simple method for generating lines with convenient
points of intersection is to pay attention to
these differences. For example, working in
slope-intercept form and choosing integral
differences in the y-intercepts (-3) and in the
slopes (8), where 3 and 8 are relatively prime,
a teacher can quickly generate two lines