How do you graph # y + 1/3x = 2# by plotting points?

2 Answers
Jun 5, 2016

Answer:

Please see below.

Explanation:

As the coefficient of #x# is #1/3#, let us pick three values of #x# which are multiple of #3# and let these be #-9,0# and #9#.

For these corresponding values of #y# will be

#y+1/3(-9)=2# or #y-3=2# or #y=5#

#y+1/3(0)=2# or #y=2#

#y+1/3(9)=2# or #y+3=2# or #y=-1#

Hence, three points through which #y+1/3x=2# passes are

#(-9,5)#, #(0,2)# and #(9,-1)#. Joining these points gives us the graph of #y+1/3x=2#

graph{y+1/3x=2 [-9.92, 10.08, -3.16, 6.84]}

Jun 5, 2016

Answer:

For an equation like this you choose two values for x and calculate y, then trace the line between these two points.

Explanation:

Let me choose x=0 and x=6 just because I can. Plugging these values into the equation I get that when x=0 y=2 and when x=6 y=0.

Now remember that this only works for linear functions. Also, in this particular case, because of the division by 3, it is easy to see that choosing values for x that are multiples of 3 will be easier to calculate the results, so while you CAN choose any value for x to plot, choosing the values carefully will help with the calculations. Just as another example looking at the graph, I see that:
#if x=3# then # y=1#
# if x=9# then #y=-1#
and
#if x=-3# then #y=4#...

You can see the tho points (0,2) and (6,0) on the graph below
graph{y+1/3x=2 [-10, 10, -5, 5]}