Question

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

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

Short answer

The required values are $A=2,B=-3,C=-3$.

Step-by-step solution

– Standard form of a linear equation.

The standard form of a linear equation is $Ax+By=C$, where $A\ge 0,A$and B are not both zero.

– Rewrite the given linear equation in the standard form.

The given equation is:

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

Multiply both sides by 3.

$3y=2x+3$

Subtract 3y and 3 from both sides.

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

Interchange both sides.

$2x-3y=-3$

– Find the required values.

Now compare the equation $2x-3y=-3$with the standard form of the linear equation $Ax+By=C$to find the values of $A,B,C$.

$\begin{array}{c}A=2\\ B=-3\\ C=-3\end{array}$

Thus, the required values are $A=2,B=-3,C=-3$.