How do you find the slope and intercept to graph $2x - 6y = 12$?

Hint: The equation of a straight line in slope-intercept form is $y = mx + c$. Where m is the value of slope and c is called the y-intercept. This is a linear equation of the first order. In this question, a linear equation is given. We will convert this equation into the form of a straight-line equation. By comparing with the standard equation we will find the value of slope and the value of intercept.

Complete step-by-step answer:
In this question, the linear equation is
$ \Rightarrow 2x - 6y = 12$
Let us subtract 2x both sides.
$ \Rightarrow 2x - 2x - 6y = 12 - 2x$
Therefore,
$ \Rightarrow - 6y = 12 - 2x$
Now, let us divide both sides by -6.
$ \Rightarrow y = \dfrac{{12 - 2x}}{{ - 6}}$
Now, simplify the above equation in standard form.
$ \Rightarrow y = \dfrac{{2x - 12}}{6}$
Let us split the denominator.
$ \Rightarrow y = \dfrac{{2x}}{6} - \dfrac{{12}}{6}$
Hence,
$ \Rightarrow y = \dfrac{x}{3} - 2$
Now, compare the above equation with a straight line equation $y = mx + c$
So, we get $m = \dfrac{1}{3}$ and $c = - 2$

Hence, the value of slope is $\dfrac{1}{3}$ and the value of intercept is -2.

Note:
Slope: The slope of a line is defined as the ratio of change in y over the change in x between any two points on the line.
$slope\left( m \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
When two coordinates are given then we will use this equation.
Let us take an example, find the slope between two points (0, 2) and (3, 4).
 $slope\left( m \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
$ \Rightarrow m = \dfrac{{4 - 2}}{{3 - 0}}$
Let us simplify it.
$ \Rightarrow m = \dfrac{2}{3}$
Some of the real-life applications of a straight line:
Used in chemistry and biology subjects.
To estimate our body weight is appropriate according to our height.
Used in the research process and preparation of the government budget.
Used in medicine and pharmacy to figure out the accurate strength of drugs.
Future contract markets and opportunities can be described through a straight line.