Question

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

Answer 1

Hint: To solve this question we should know about linear equations.
Linear equation: The equation having the highest power of its variable is one.
General linear equation in standard form is $Ax + By = C$ .
Here, $A,B\,and\,C$ is constant.

 Complete step-by-step solution:
As given in question,
The equation is, $y = - \dfrac{3}{2}x + 3$ .
As we know,
The equation of a line in standard form is $Ax + By = C$ .
Where $A$ is a positive integer and $B,C$ are integers given.
So, we will go step by step to solve it:
$y = - \dfrac{3}{2}x + 3$
Step1: Multiply all terms by $2$
 $2y = - 3x + 6$
Step 2: Add $3x$ to both sides
 $3x + 2y = 6$
As our solved equation resembles a standard form.

Hence $3x + 2y = 6$ is standard form of given equation.

Note: There are many general form of linear equation:
General form: $Ax + By + C = 0$
Point-slope form: $y - {y_1} = m(x - {x_1})$
Slope intercept form: $y = mx + c$
A linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.
The solution of such an equation are the values that, when substituted for the unknowns, make the equality true.