Question

How do you write $ y = \dfrac{2}{3}x - 7 $ in standard form?

Answer 1

Hint: We can observe that the given equation is a linear equation in two variables. Because there are two variables $ x $ and $ y $ , and their relationship is linear, meaning that the highest power of the terms in the equation is $ 1 $ .

Complete step-by-step answer:
The standard form of a linear equation in two variables is $ ax + by = c $ , where $ a,{\text{ }}b{\text{ and }}c $ are non-zero constants and $ a > 0 $ . The given equation is, $ y = \dfrac{2}{3}x - 7 $ . We will bring the $ x $ and $ y $ terms to one side and the constant term to one side to write the equation in the standard form.
 $ \Rightarrow y - \dfrac{2}{3}x = - 7 $
We can further simplify the equation by multiplying both sides with $ 3 $ to get $ 3y - 2x = - 21 $ . Moreover, we can multiply with $ - 1 $ and rearrange the terms to get the standard form.
 $ \Rightarrow 2x - 3y = 21 $
Hence the standard form of the equation is $ 2x - 3y = 21 $ .
So, the correct answer is “ $ 2x - 3y = 21 $ ”.

Note: The procedure to get the standard form of a linear equation in two variables can be condensed into the following steps:
1. Make sure that the equation is linear in $ x{\text{ and }}y $ .
2. Separate the constant terms on one side and the variable terms on one side.
3. Multiply the entire equation with the least common multiple (LCM) of the denominators and simplify.
4. If the coefficient of the $ x $ term is negative multiply both sides with $ - 1 $ and rearrange the terms to comply with the standard form.