What pattern will result from plotting all points x, y that satisfy an equation in the form ax+by=c

You only need to plot two points, because the pattern is a
straight line, and any two points on it define the entire line.

-- The slope of the line is [ -a/b ] .

-- The line intersects the x-axis at [ x = c/a ] .

-- The line intersects the y-axis at [ y = c/b ] .