How do you rewrite $2x - 3y = 12$ in slope intercept form ?

Hint:The slope intercept form of a line is given as $y = mx + c$ where “m” is the slope of the line and “c” is the intercept (mainly y intercept when $x = 0$). Convert the given equation of line into slope intercept form with help of algebraic operations like addition, subtraction, division etc.

Complete step by step answer:
The given equation is an equation of straight line which is expressed in the standard equation of straight line, and we are asked to convert it into slope intercept form which is given as following $y = mx + c$ where “m” is the slope of the line and “c” is its intercept.
Now, coming to the given equation of line
$2x - 3y = 12$
Firstly sending the independent variable (x) to the right hand side of the equation by subtracting $2x$ from both sides of the equation,
$2x - 3y - 2x = 12 - 2x \\
\Rightarrow - 3y = 12 - 2x \\ $
Now as we can see in the general equation of line in slope intercept form, the left hand side of the equation only consists of the dependent variable and right hand side consists of independent variable as well as constant. Multiplying with $ - 1$ and dividing with $3$ both sides of the equation, we will get
\[- 1 \times \dfrac{{ - 3y}}{3} = - 1 \times \dfrac{{(12 - 2x)}}{3} \\
\Rightarrow y = \dfrac{2}{3}x - \dfrac{{12}}{3} \\
\therefore y = \dfrac{2}{3}x - 4 \\ \]
Hence, $y = \dfrac{2}{3}x - 4$ is the slope intercept form of the equation $2x - 3y = 12$.

Note: Equation consists of two variables and is of one degree represents a line, and equation of a line can be written in many forms, in which slope intercept form is one of them. If we have any one form of equation of line written then we can write its other forms too by doing some simple algebra.