Question 146799

Let's graph the 1st equation {{{y=x+4}}}:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,x+4)
)}}} Graph of {{{y=x+4}}}



Now <font size="4"><b>only</b></font> graph the portion of the line that is less than or equal to 2 compared to the x-axis



So the new graph looks like this:

{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,0),
line(-10,-6,-9,-5),
line(-9,-5,-8,-4),
line(-8,-4,-7,-3),
line(-7,-3,-6,-2),
line(-6,-2,-5,-1),
line(-5,-1,-4,0),
line(-4,0,-3,1),
line(-3,1,-2,2),
line(-2,2,-1,3),
line(-1,3,0,4),
line(0,4,1,5),
line(1,5,2,6)
)}}} Graph of {{{y=x+4}}} with the restriction {{{x<=2}}}. Note: there is a closed circle at the endpoint.



Let's graph the 2nd equation {{{y=3x}}}:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,3x)
)}}} Graph of {{{y=3x}}}



Now <font size="4"><b>only</b></font> graph the portion of the line that is greater than 2 compared to the x-axis



So the new graph looks like this:

{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,0),
line(2,6,3,9),
line(3,9,4,12),
line(4,12,5,15),
line(5,15,6,18),
line(6,18,7,21),
line(7,21,8,24),
line(8,24,9,27),
line(9,27,10,30)
)}}} Graph of {{{y=3x}}} with the restriction {{{x>2}}}. Note: there is an open circle at the endpoint.



Now let's graph the equations together:



{{{drawing(500,500,-10,10,-10,10,
grid(0),
graph(500,500,-10,10,-10,10,0),

red(line(-10,-6,-9,-5)),
red(line(-9,-5,-8,-4)),
red(line(-8,-4,-7,-3)),
red(line(-7,-3,-6,-2)),
red(line(-6,-2,-5,-1)),
red(line(-5,-1,-4,0)),
red(line(-4,0,-3,1)),
red(line(-3,1,-2,2)),
red(line(-2,2,-1,3)),
red(line(-1,3,0,4)),
red(line(0,4,1,5)),
red(line(1,5,2,6)),
 green(line(2,6,3,9)),
green(line(3,9,4,12)),
green(line(4,12,5,15)),
green(line(5,15,6,18)),
green(line(6,18,7,21)),
green(line(7,21,8,24)),
green(line(8,24,9,27)),
green(line(9,27,10,30))
)}}} Graph of {{{y=x+4}}} with the restriction of {{{x<=2}}} (red). Graph of {{{y=3x}}} with the restriction of {{{x>2}}} (green).