The first thing we have to do here is to organize the function in its base form: #y=f(x)#. Send #y# to the right side of the equation summing and #-7# to the left side, also summing. This is the same as adding #(y+7)# to both sides of the equation:
#3xcancel(-y+y)+7=cancel(-7+7)+y#
#3x+7=y#, or #y=3x+7#.
In order to make the table, we must solve this function creating values for #x# close to the origin. Since this is a linear function, we need at least 2 points to make the line, but let's use 3, just to guarantee. I chose #-1, 0# and #1#:
#{:
(x,,y),
(-1,,3(-1)+7=-3+7=4),
(0,,3(0)+7=0+7=7),
(1,,3(1)+7=3+7=10)
:}#
Checking:
graph{3x+7 [-2., 2, -5, 12]}
