Question

How do you write $y = \dfrac{7}{2}x - 6$ in standard form?

Answer 1

Here, we are required to solve the given linear equation which is in slope intercept form. We will compare this equation to the standard form of a linear equation in two variables and then, we will write this equation in the standard form by comparing the variables and the coefficients.

Complete step by step solution:
The given equation is $y = \dfrac{7}{2}x - 6$
We can see that this is a linear equation having two variables i.e. $x$ and $y$. Thus, we are required to write this equation in the standard form of linear equation in two variables.
As we know, the standard form of linear equation in two variables is $Ax + By = C$
Now, given equation is:
$y = \dfrac{7}{2}x - 6$
Now, multiplying both sides by 2 in order to remove the fraction from the coefficient of $x$, we get,
$2y = 2 \times \dfrac{7}{2}x - \left( {2 \times 6} \right)$
$\Rightarrow 2y = 7x - 12$
Subtracting $2y$ from both sides, we get
$\Rightarrow 0 = 7x - 12 - 2y$
And, adding 12 on both sides, we get,
$\Rightarrow 7x - 2y = 12$
Clearly, this is in the standard form.

Therefore, we can write $y = \dfrac{7}{2}x - 6$ as $7x - 2y = 12$ in the standard form.
Hence, this is the required answer.

Note:
As we can notice, the given equation to be solved is a linear equation having two variables. A linear equation in two variables is an equation which can be written in the form of $Ax + By = C$ where $x$ and $y$ are the variables and $A,B$ and $C$ are the three integers and all of them should not be equal to zero. Now, in linear equations, the variable has the highest power 1. This is because of the fact that if the power becomes 2 then, it would not be called a linear equation. Else, it would turn out to be a quadratic one and there will be two solutions for the variable. Similarly, if the power becomes 3, then it would be a cubic equation and then, the variable would have 3 solutions or values.