How I solve $-2x + 7y + 6 = 20$? I've been having trouble trying to figure out this linear equation. I only know how to calculate with two variables and no constant, I'm not good at figuring out problems with new "formats" if that's the right word.
I tried subtracting $6$ from both sides, but I don't think that's the right way to do it. I think I'm supposed to subtract $7y$ from both sides? Could you help me learn how to graph and solve this equation?
 A: One of the most common way to graph a function like this is to write it in what is known as slope-intercept form. Slope-intercept form is of the form
$$y=mx+b,$$
where $m$ is the slope, and $b$ is the $y$-intercept. For your problem, we need to solve for $y$:
\begin{align*}
-2x+7y+6&=20\\
-2x+7y&=14&\text{by subtracting $6$ to both sides}\\
7y&=2x+14&\text{by adding $2x$ to both sides}\\
y&=\frac27x+2&\text{by dividing by $7$ on both sides}
\end{align*}
This is an equation of a line in slope-intercept form. The slope is $2/7$ and the $y$-intercept is $2$.
To graph it, first plot the $y$-intercept, which is $(0,2)$. To find the next point on our line, we use the slope. You may have heard of "slope is rise over run". In our case, the slope is $2/7$, so our "rise" is $2$, and our "run" is $7$. That is, starting from $(0,2)$, we go up by $2$, and go to the right by $7$, giving us a second point of $(7,4)$. Connecting $(0,2)$ and $(7,4)$ gives us our line.
A: By subtracting 6 from both sides you will get:
-2x + 7y = 14.
To plot this equation on the graph, assume any value of one of the variables and find the other.
Assume x=0, then you will get 7y = 14. Therefore y = 2.
So, First point becomes (0, 2).
Similarly assume y=0, then you will get -2x=14. Therefore x=-7.
So second point becomes (-7, 0)
Connect these two points on the x-y plane.
You can choose and other value of x or y, you will get the resultant point on the graph of your equation.
