Question

How do you write $y = \dfrac{2}{3}x - 2$ in standard form?

Answer 1

We use the concept of the standard form of a linear equation and solve for the value of the equation. Bring all the variables to the left side of the equation keeping the constant value on the right side of the equation. After that take L.C.M. on the left side and then cross multiply. After that multiply both sides by -1 to get the desired result.
The standard form of a linear equation is given by $Ax + By = C$ where A is non-negative and A, B and C are constant values.

Complete step-by-step answer:
We have to find the standard form of $y = \dfrac{2}{3}x - 2$.
Now bring all variables to the left-hand side of the equation and all constant values to the right-hand side of the equation.
$\Rightarrow y - \dfrac{2}{3}x = - 2$
Take L.C.M. on the left side of the equation,
$\Rightarrow \dfrac{{3y - 2x}}{3} = - 2$
Cross multiply the terms,
$\Rightarrow 3y - 2x = - 6$
Multiply both sides of the equation by -1,
$\Rightarrow 2x - 3y = 6$
Now we can say that this equation matches the form $Ax + By = C$, so the equation $2x - 3y = 6$ is in standard form.

Hence, the standard form of $y = \dfrac{2}{3}x - 2$ is $2x - 3y = 6$.

Note:
Students are likely to make mistakes while shifting the values from one side of the equation to another side of the equation as they forget to change the sign of the value shifted. Keep in mind we always change the sign of the value from positive to negative and vice versa when shifting values from one side of the equation to another side of the equation.
Also, many students bring all the terms on one side i.e., the left-hand side of the equation thinking the standard form must have 0 on the right-hand side of the equation which is wrong, use the definition of the standard form of a linear equation, and then proceed.