Check the graph below, please.
1) Let's first set tables to get the value of y, since the values of x can be chosen in an arbitrary way.
x +2y =6 Rewriting it as a slope-intercept form to better visualize it
2y = 6 - x
y=3-x/2
x| y
-1 3.5
0 3
1 2.5
(-1, 3.5), (0,3), (1, 2.5) Points to be located
And for the second equation:
y-2=-2(x-3) Rewriting it as a slope-intercept form to better visualize it
y =-2x+6+2
y=-2x +8
x | y
-1 10
0 8
1 6
(-1,10), (0,8) , (1,6) Plots to be located
2) Now we can plot that graph tracing a line through those points:
Notice that both equations have one common point: