Question

How do you write the equation $y = 3x - 5$ in standard form and identify $A,B{\text{ and C}}$?

Answer 1

Hint: The standard form of the linear equation is $Ax + By = C$, we are going simply relocate the terms containing variable to the one side of the equation and the remaining constant terms to the other side of the equation to convert the given equation into the standard form. Thus we will get the required equation.

Complete step by step answer:
Start by writing the given equation:
$ \Rightarrow y = 3x - 5$
Now, to solve this question is we have to relocate the terms containing variables to one side of the equation. So we get,
$ \Rightarrow y - 3x = - 5$
Now adjust the equation according to the standard form of equation and then rewrite it.
We can have
$ \Rightarrow - 3x + y = - 5$
Here is the equation in standard form is: $ - 3x + y = - 5$
Which is of the standard form $Ax + By = C$.
From this we can also conclude the values of variables $A,B{\text{ and C}}$, where $A$ and $B$ are the coefficients of variables x and y and C is the constant value:
$A = - 3$, $B = 1$ and $C = - 5$

Note: Remember it depends upon what information the problem gives you. You need to read it carefully.
Did it give you what looks like $2$ ordered pairs? If yes, then you would:
$1)$ Find the slope using the $x$ & $y$ values from the ordered pairs.
$2)$ Use either slope-intercept form or point-slope form to get your initial equation.
$3)$ Convert your equation to standard form.
Or, if the problem gives you a slope (a rate of change) and $1$ ordered pair? If this is the case, then you can just do steps $2$ and $3$ above.