equation to linear function I'm doing homework and I've been given a line as the equation $7x-6y=5.$
I need to make a function $y = f(x)$ of this that corresponds to the equation.
What I know at this point is that I need to know what the $a$ and $b$ are in $y = ax + b.$
I also know of the formula to calculate $a$, which is $\,\dfrac{y_{b} - y_{a}}{  x_{b} - x_{a}}.\,$ I'm also wondering what a is called in English? It's "richtingscoëfficient" in Dutch.
I've tried to fill in the equation by using random numbers as x to calculate y, and using the formula $\dfrac{y_{b} - y_{a}}{ x_{b} - x_{a}}$ , but when I used the formula twice it turned out the answers were different from each other, which I don't understand, because it seemed logical to me that the answer had to be equal.
Please try to keep the answer simple, so do not use many symbols because I hardly know any yet.
Can someone correct my comment? I don't know what to fill in as tags, and how to put the formula's in the nice latex.
 A: Try simple and avoid teacher jargon, it's used for make your remember it, but in fact they are not associated with something real.
Try to solve it as a equation where the unknown is y 
$\begin{array}{l}
7x - 6y = 5\\
 - 6y = 5 - 7x\\
6y = 7x - 5\\
y = \frac{{7x - 5}}{6} = \frac{7}{6}x - \frac{5}{6}
\end{array}$
Then:
$f(x) = \frac{7}{6}x - \frac{5}{6}$
A: You can do it like this. Let's begin with the expression you have:
$$
7x-6y=5
$$
Adding the term $-7x$ to both sides, they remain equal and become
$$
7x-6y-7x=5-7x
$$
that is
$$
-6y=5-7x
$$
Now let's multiply both sides of this equation by $-\dfrac{1}{6}$. We get:
$$
y=\dfrac{7}{6}x-\dfrac{5}{6}
$$
which is in the form you wanted. By the way, the number $\dfrac{7}{6}$ is called the slope of the line, which is a measure of its inclination.
A: The $a$ is the $\textit{slope}$ of the linear function, which is just a measure of the rate of change of the line.
$7x-6y=5\implies-6y=-7x+5 \implies 6y=7x-5 \implies y=\dfrac{7x-5}{6}$
In this case, $\dfrac{7}{6}$ is the slope.
