How do you graph #f(x)= -1/2x-3# using a table of values?

For example, say you have have #x# values of #-1, 0,# and #1# in your table; to find their #y# values, input your #x# values in place of #x# in the equation, like so:

#f(x)=−1/2x−3#

#f(x)=−1/2#(-#1#)#−3#

Then solve for #y#.

#y=-5/2# or #y=-2.5#

Repeat this for #x# values #0# and #1#.

#f(x)=−1/2(0)−3#

Solve for #y#.

#y=-3#

Finally, for #1#:

#f(x)=−1/2x−3#

#f(x)=−1/2(1)−3#

Solve for #y#.

#y=-7/2# or #y=-3.5#.

Your final results in a table of values would look like this:

and if your curious, the graph would look like this:
graph{((-1/2)x)-3 [-5.666, 4.334, -4.02, 0.98]}

As this is a strait line graph then technically you only need 2 points and then you can draw a line between and beyond them. However I would recommend 3 points. If they all line up then there is every chance that your calculated values are correct.

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The problem comes when you have a graph of a line that is not strait. You then have to produce a table for a number of points as needs dictate. These points will then be marked on the graph paper and connected by a curved line which (if free hand) you will have to produce as best as your 'eye' permits.

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#color(brown)("Although my example of a table is for more than three points it is")# #color(brown)("the sort of thing you would have to produce for a non strait line")# #color(brown)("graph.")#

#color(green)("The number of calculated point being down to your choice. For")# #color(green)("ease of construct I used Excel.")#

If the source equation is complex then this type of layout (stepwise construct) really helps.