Question

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

Answer 1

Simply input your values for `x` into the equation to obtain the values of `y`. (Since `f(x)=` is the same as `y=`.)

Explanation:

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]}

Answer 2

Just another table construct example with comments

Explanation:

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.