#20x+80y=0# is the standard form for a linear equation. Solve for #y# in order to convert the equation to slope-intercept form, #y=mx+b#, where #m# is the slope and #b# is the y-intercept.
#20x+80y=0#
Subtract #20x# from both sides.
#80y=-20x#
Divide both sides by #80#.
#y=(-20x)/80=#
#y=-1/4x#
The slope, #m# is #-1/4# and the y-intercept, #b# is #0#.
Graphing the equation
#y=-1/4x#
Substitute #0# for #x#.
#y=-1/4(0)=0#
This gives us a point at the origin, #0,0#.
To use the slope to determine other points, you can use the slope of #-1/4#. Starting at the origin, go up #1# and over #-4#, keeping going as far as you want. You can also start at the origin and go down #1# and over #4#, keeping going as far as you want. You really only need two points to graph a straight line.
You can also substitute values for #x# into the equation and solve for #y#.
If #x=4,# # y=-1#
If #x=-4,# # y=1#
Below is how the graph of #y=-1/4x# would look.
graph{y=-1/4x [-10, 10, -5, 5]}
