Question

How do you graph `3x - y = -7` using a table of values?

Answer 1

Rewrite the function as `y=3x-7` then solve it using values for x close to the origin.

`{: ("x",,"y"), (-1,,4), (0,,7), (1,,10) :}`

Explanation:

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]}