How do you write $ y = \dfrac{4}{3}x + \dfrac{2}{3} $ in standard form?

Hint: We are given an equation of the form of the equation of line. We have to convert it into the standard form of the line. The standard form of the equation of line is: Ax+By=C. A cannot be negative. A, B and C should all be integers. The first thing we should do is move the x over to the left part of the equation. Then we will reorder it and then we need to make it sure that the number that’s before the x (A) is positive. We can do this by multiplying both parts by -1. Now all we need to do is make A, B and C integers. We can also do this by multiplying by the l.c.m of all the denominators. By this we will get the required equation.

Complete step-by-step solution:
Step1: We are given an equation i.e. $ y = \dfrac{4}{3}x + \dfrac{2}{3} $ . To create the standard we don’t need any fractions and x, y should be on the same side. Firstly we will multiply both sides by 3. We will get:
 $ \Rightarrow 3y = 4x + 2 $ .
Step2: Now we will subtract $ 4x $ from both the sides we will get:
 $ \Rightarrow 3y - 4x = 4x + 2 - 4x $
On rearrangement we will get:
 $ \Rightarrow 3y - 4x = 2 $
Now we will multiply every term by $ - 1 $ to make the ‘x’ coefficient positive. We will get:
 $ \Rightarrow 4x - 3y = - 2 $

Hence the standard form of the equation is $ 4x - 3y = - 2 $

Note: The equation shows the standard equation of line and this has to be converted into the standard linear equation form i.e. of the form Ax+By=C. For this form students need to keep two things in mind i.e. the coefficient of x should be positive. X and y should be one side and there should be no fraction. By following these tips we can convert any equation into the standard form.