Summarize a strategy that can be used to graph ax+by+c=0

You could rearrange the equation in slope intercept form.
Graph the y-intercept first. From the y-intercept count the rise/run (slope) and plot another point. Continue doing this until you have enough points to drawn a line.
Ax + By + C = 0
Subtract Ax and C from both sides
By = -Ax - C
Divide both sides by B
y = -(A/B)x - (C/B) where (A/B) is the slope and (C/B) is the y-intercept