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

Jun 24, 2016

Rewrite the function as $y = 3 x - 7$ 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: $y = f \left(x\right)$. Send $y$ to the right side of the equation summing and $- 7$ to the left side, also summing. This is the same as adding $\left(y + 7\right)$ to both sides of the equation:
$3 x \cancel{- y + y} + 7 = \cancel{- 7 + 7} + y$
$3 x + 7 = y$, or $y = 3 x + 7$.

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]}