Question 519378
<pre>
            5x - 8y = 40

1.  Make a table of arbitrary values:

 x |   y   
 4 | 
 2 | 
-2 | 
-4 | 
 Calculate the other variable values:

{{{matrix(5,4,
5(4)-8y=40,      5(2)-8y=40,       5(-2)-8y=40,     5(-4)-8y=40,     
 20-8y=40,        10-8y=40,        -10-8y=40,      -20-8y=40, 
   -8y=20,          -8y=30,          -8y=50,             -8y=60, 
     y=20/(-8),       y=30/(-8),       y=50/(-8),          y=60/(-8),
     y=-2.5,          y=-3.75,         y=-6.25,            y=-7.5)}}}

Fill in the table:

 x |   y   
 4 | -2.5
 2 | -3.75
-2 | -6.25
-4 | -7.5

Plot the points:

{{{drawing(400,880/3,-5,10,-8,3, graph(400,880/3,-5,10,-8,3),
circle(4,-2.5,.1),locate(4,-2.5,"(4,-2.5)"),
circle(2,-3.75,.1),locate(2,-3.75,"(2,-3.75)"),
circle(-2,-6.25,.1),locate(-2,-6.25,"(-2,-6.25)"),
circle(-4,-7.5,.1),locate(-4,-7.5,"(-4,-7.5)")



 )}}}

Draw a line through them:

{{{drawing(400,880/3,-5,10,-8,3, graph(400,880/3,-5,10,-8,3),
circle(4,-2.5,.1),locate(4,-2.5,"(4,-2.5)"),
circle(2,-3.75,.1),locate(2,-3.75,"(2,-3.75)"),
circle(-2,-6.25,.1),locate(-2,-6.25,"(-2,-6.25)"),
circle(-4,-7.5,.1),locate(-4,-7.5,"(-4,-7.5)"), blue(line(-8,-10,16,5))



 )}}}



2.  Get the equation in slope-intercept form y = mx+b

  5x - 8y = 40
      -8y = -5x + 40
        y = {{{5/8}}}x - 5

The slope is {{{5/8}}} and the y-intercept is (0,-5)

Start at the y-intercept, draw a vertical line upward
5 units (the numerator of the slope), and from there
draw a horizontal line rightward 8 units (the denominator
of the slope):

{{{drawing(400,880/3,-5,10,-8,3, graph(400,880/3,-5,10,-8,3),

green(line(0,-5,0,0), line(0,0,8,0)) )}}}

Draw a line through the y-intercept (0,-5) and the end of the vertical
line:

{{{drawing(400,880/3,-5,10,-8,3, graph(400,880/3,-5,10,-8,3),
blue(line(-8,-10,16,5)),

green(line(0,-5,0,0), line(0,0,8,0)) )}}}


3.  Find the two intercepts

To find the x-intercept, we substitute 0 for y:

  5x - 8y = 40
5x - 8(0) = 40
  5x - 0  = 40
       5x = 40
        x = 8, so the x-intercept is (8,0)

To find the y-intercept, we substitute 0 for x:

  5x - 8y = 40
5(0) - 8y = 40
   0 - 8y = 40
      -8y = 40
        y = -5, so the y-intercept is (0,-5).

Plot the intercepts:

{{{drawing(400,880/3,-5,10,-8,3, graph(400,880/3,-5,10,-8,3),
circle(0,-5,.2),circle(8,0,.2), locate(0,-5,"(0,-5)"),
locate(6.2,.8,"(8,0)")


 )}}}

Draw a line through those two intercepts:

{{{drawing(400,880/3,-5,10,-8,3, graph(400,880/3,-5,10,-8,3),
circle(0,-5,.2),circle(8,0,.2), locate(0,-5,"(0,-5)"),
locate(6.2,.8,"(8,0)"), blue(line(-8,-10,16,5))



 )}}}

Edwin</pre>