Question

How do you write $ y + 7 = \dfrac{9}{{10}}(x + 3) $ in standard form?

Answer 1

Hint: In order to convert the above equation into the standard linear equation $ Ax + By = C $ ,first multiply the both sides of the equation with the value $ 10 $ and use distributive law $ A(B + C) = AB + AC $ .Combine like term by transposing term having $ x\,and\,y $ variable on the left hand side and constant terms on the right hand side to get your required result.

Complete step-by-step answer:
We are given a equation having variable $ x $ and $ y $ i.e. $ y + 7 = \dfrac{9}{{10}}(x + 3) $
The standard form of linear equation in two variable is equal to $ Ax + By = C $
Now to convert our given equation in the standard form, we will apply some steps .
 $ y + 7 = \dfrac{9}{{10}}(x + 3) $
Multiplying both sides of the equation with $ \dfrac{{10}}{9} $ ,we get
 \[
  10(y + 7) = \dfrac{9}{{10}}(x + 3)(10) \\
  10(y + 7) = 9(x + 3) \;
 \]
Using distributive law which states that $ A(B + C) = AB + AC $
 \[
  10(y + 7) = 9(x + 3) \\
  10y + 70 = 9x + 27 \;
 \]
Now combining like terms on both of the sides. Terms having $ x $ and $ y $ will on the Left-Hand side of the equation and constant terms on the right-hand side .
Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term get reversed .In our case , $ 70 $ on the left hand side will become $ - 70 $ on the right hand side .
 \[
   - 9x + 10y = 27 - 70 \\
   - 9x + 10y = - 43 \;
 \]
Multiplying with $ ( - 1) $ on both side of the equation we get,
 \[9x - 10y = 43\]
Therefore, the equation in the standard form is equivalent to \[9x - 10y = 43\]
So, the correct answer is “ \[9x - 10y = 43\] ”.

Note: Linear Equation In two variables: A linear equation in two variables is an equation which can be represented in the form of $ ax + by = c $ where $ x $ and $ y $ is the unknown variable and c are the numbers known .