Question

How do you write $y = \dfrac{3}{4}x + \dfrac{1}{2}$ 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. Take LCM on the right side of the equation and cross multiply the values from both sides. Bring all the variables to the left side of the equation keeping the constant value in right side of the equation.

• 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 $y = \dfrac{3}{4}x + \dfrac{1}{2}$
We first take LCM of the terms in right hand side of the equation
$\Rightarrow y = \dfrac{{3x + 2}}{4}$
Cross multiply denominator from right hand side of the equation to left hand side of the equation
$\Rightarrow 4y = 3x + 2$
Now bring all variables to the left hand side of the equation and all constant values to the right hand side of the equation.
$\Rightarrow - 3x + 4y = 2$
Multiply both sides of the equation by -1
$\Rightarrow - 3x \times ( - 1) + 4y( - 1) = 2( - 1)$
$\Rightarrow 3x - 4y = - 2$
We can write the above equation as $3x + ( - 4)y = - 2$
Now we can say that this equation matches the form $Ax + By = C$, so the equation $3x + ( - 4)y = - 2$ is in standard form.

$\therefore$Standard form of the linear equation $y = \dfrac{3}{4}x + \dfrac{1}{2}$ is $3x + ( - 4)y = - 2$

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. left hand side of the equation thinking standard form must have 0 in right hand side of the equation which is wrong, use the definition of standard form of linear equation and then proceed.