Question 370441
my homework says to "identify three more points on the line that passes through the point (-4,-2) & has a slope of 2/3" i have no clue what it is asking
<pre>
Plot the point (-4,-2):

{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),

circle(-4,-2,.1), locate(-4-1.8,-2+.25,"(-4,-2)")  )}}}

The denominator of the slope 2/3 is 3, so draw a horizontal line 
3 units right from the point (-4,-2).  I'll draw it in green:

{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),
green(line(-4,-2,-1,-2)),
circle(-4,-2,.1), locate(-4-1.8,-2+.25,"(-4,-2)")  )}}}

The numerator of the slope 2/3 is 2, so draw a vertical line 
2 units right from the end of that green line up 2 units.  
I'll also draw it in green:

{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),
green(line(-4,-2,-1,-2),line(-1,-2,-1,0)),
circle(-4,-2,.1), locate(-4-1.8,-2+.25,"(-4,-2)")  )}}}

That's the point (-1,0), so that's one point.

Now do the same thing from the point (-1,0).  Draw a horizontal line
3 units right and 2 units up, just as you did with the first point.

{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),
green(line(-4,-2,-1,-2),line(-1,-2,-1,0), locate(1-1.8,0+.25,"(1,0)"), 

line(-1,0,2,0),line(2,0,2,2)

),locate(-1-1.3,0+.6,"(-1,0)"),

circle(-4,-2,.1), locate(-4-1.8,-2+.25,"(-4,-2)")  )}}}


That's the point (2,2), so that's another point.

Now do the same thing from the point (2,2).  Draw a horizontal line
3 units right and 2 units up, just as you did with the first point.

{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),
green(line(-4,-2,-1,-2),line(-1,-2,-1,0),
line(2,2,5,2),line(5,2,5,4),
line(-1,0,2,0),line(2,0,2,2)

),locate(2-1.4,2+.35,"(2,2)"), locate(-1-1.3,0+.6,"(-1,0)"),

circle(-4,-2,.1), locate(-4-1.8,-2+.25,"(-4,-2)")  )}}}

That's the point (5,4), so that's another point, and you can see they're
all on the same line

{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),
green(line(-4,-2,-1,-2),line(-1,-2,-1,0),
line(2,2,5,2),line(5,2,5,4),
line(-1,0,2,0),line(2,0,2,2)
), line(11,8,-10,-6), locate(2-1.4,2+.35,"(2,2)"), locate(-1-1.3,0+.6,"(-1,0)"),
locate(5-1.4,4+.35,"(5,4)"),

circle(-4,-2,.1), locate(-4-1.8,-2+.25,"(-4,-2)")  )}}}

Edwin</pre>