Question 277186
please help show my son how to create a graph from the following functions. y=x+5
<pre><font size = 4 color = "indigo"><b>
Start with a set of axes:

{{{graph(400,400,-10,10,-10,10)}}}

substitute 

x = 1 

into that equation

y = (1) + 5
y = 1 + 5
y = 6

Write the ordered pair (x,y) = (1,6)

Plot that ordered by drawing a vertical green line 
through 1 on the x axis (since x=1) and a red line 
through 6 on the y-axis (since y=6), like this:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),

green(line(1,-11,1,11)), red(line(-11,6,11,6)) )}}}

Mark the point where they cross, and label it {{{"(1,6)"}}}

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
green(line(1,-11,1,11)), red(line(-11,6,11,6)), locate(1,6,"(1,6)"),
line(1+.1,6,1-.1,6), line(1,6+.1,1,6-.1), line(1+.1,6+.1,1-.1,6-.1), line(1+.1,6-.1,1-.1,6+.1) )}}}


Now erase the green and red lines.

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10), locate(1,6,"(1,6)"),
line(1+.1,6,1-.1,6), line(1,6+.1,1,6-.1), line(1+.1,6+.1,1-.1,6-.1), line(1+.1,6-.1,1-.1,6+.1) )}}}


----

substitute 

x = -2 

into that equation

y = (-2) + 5
y = -2 + 5
y = 3

Write the ordered pair (x,y) = (-2,3)

Plot that ordered by drawing a vertical green line 
through -2 on the x axis (since x=-2) and a red line 
through 3 on the y-axis (since y=3), like this:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
locate(1,6,"(1,6)"),
line(1+.1,6,1-.1,6), line(1,6+.1,1,6-.1), line(1+.1,6+.1,1-.1,6-.1), line(1+.1,6-.1,1-.1,6+.1),
green(line(-2,-11,-2,11)), red(line(-11,3,11,3)) )}}} 

Mark the point where they cross, and label it {{{"(-2,3)"}}}

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
green(line(-2,-11,-2,11)), red(line(-11,3,11,3)),  locate(-4.7,3,"(-2,3)"),
line(-2+.1,3,-2-.1,3), line(-2,3+.1,-2,3-.1), line(-2+.1,3+.1,-2-.1,3-.1), line(-2+.1,3-.1,-2-.1,3+.1), locate(1,6,"(1,6)"),
line(1+.1,6,1-.1,6), line(1,6+.1,1,6-.1), line(1+.1,6+.1,1-.1,6-.1), line(1+.1,6-.1,1-.1,6+.1) )}}}


Now erase the green and red lines.

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
 locate(-4.7,3,"(-2,3)"),
line(-2+.1,3,-2-.1,3), line(-2,3+.1,-2,3-.1), line(-2+.1,3+.1,-2-.1,3-.1), line(-2+.1,3-.1,-2-.1,3+.1), locate(1,6,"(1,6)"),
line(1+.1,6,1-.1,6), line(1,6+.1,1,6-.1), line(1+.1,6+.1,1-.1,6-.1), line(1+.1,6-.1,1-.1,6+.1) )}}}


Now draw a blue line through both those points:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10,11,12,x+5),
 locate(-4.7,3,"(-2,3)"),
line(-2+.1,3,-2-.1,3), line(-2,3+.1,-2,3-.1), line(-2+.1,3+.1,-2-.1,3-.1), line(-2+.1,3-.1,-2-.1,3+.1), locate(1,6,"(1,6)"),
line(1+.1,6,1-.1,6), line(1,6+.1,1,6-.1), line(1+.1,6+.1,1-.1,6-.1), line(1+.1,6-.1,1-.1,6+.1) )}}}

That blue line is the graph of the equation {{{y=5+5}}}.  Notice that the
values I picked for x, 1 and -2 were completely arbitrary!  Picking any 
value of x will do, You will get different points, but they will always fall
right on that same blue line.  The other tutor picked 0 and -5, and (0,5) and
(-5,0) are also on this line.

Edwin</pre>