Question

Write each equation in standard form. Identify A, B, and C.

$y=\frac{1}{2}x-3$

Short answer

The standard form of the equation is $x-2y=6$ and $A=1, B=-2, C=6$.

Step-by-step solution

Step-1 – Apply the concept of Standard form of equation 

Any linear equation with variables xand ycan be expressed in the standard form as:

$Ax+By=C$

Where A, B, and C are all integers with greatest common factor as 1.

Step-2 – Convert the equation into standard form

Consider the given equation.

$y=\frac{1}{2}x-3$

To convert it into standard form, subtract $\frac{1}{2}x$on both sides of equation.

$\begin{array}{c}y-\frac{1}{2}x=\frac{1}{2}x-3-\frac{1}{2}x\\ -\frac{1}{2}x+y=-3\end{array}$

Now, multiply whole equation by $-2$.

$\begin{array}{c}\left(-2\right)\left(-\frac{1}{2}x+y\right)=\left(-2\right)\left(-3\right)\\ x-2y=6\end{array}$

Thus, the standard form of the equation is $x-2y=6$.

Step-3 – Identification of A, B, and C

Comparing $x-2y=6$with standard form $Ax+By=C$, we get

$\begin{array}{l}A=1\\ B=-2\\ C=6\end{array}$

Hence, the standard form of the equation is $x-2y=6$ and $A=1, B=-2, C=6$.