Answer

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**Hint:**In this question, we have to find the slope and intercept for the given equation. For this use the formula $y=mx+c$ and substitute all the values that have been given and you will get the required equation. Therefore, by using the equation we can find the slope and intercept for the given equation.

**Complete step by step solution:**

We asked to find the slope and intercept for the given equation.

$2x-3y=12$

Rewrite the given equation in slope intercept form as slope intercept form is

$y=mx+c$

Where $'m'$ is the slope and $'c'$ is the intercept.

Now, subtract $2x$ from both sides of the given equation $2x-3y=12$ or shift left hand side $2x$ to right hand side so that it becomes $-2x$

Therefore, we have

$-3y=12-2x$

Then, divide each term by $-3$ and simplify the above equation we get,

$\dfrac{-3y}{-3}=\dfrac{12}{-3}+\dfrac{-2x}{-3}$

$\dfrac{-3y}{-3}=\dfrac{12}{-3}+\dfrac{-2x}{-3}$

After cancelling the common factor of $-3$ we get,

$y=\dfrac{12}{-3}+\dfrac{-2x}{-3}$

Now, dividing $12$ by $-3$ we have,

$y=-4+\dfrac{-2x}{-3}$

We know that dividing two negative values results in a positive value. Therefore above equation can be written as,

$y=-4+\dfrac{2x}{3}$

Now, rearranging the above equation we get,

$y=\dfrac{2x}{3}-4$

Now comparing the above equation with general equation of slope intercept form that is

$y=mx+c$

Therefore, $m=\dfrac{2}{3}$ and $c=-4$

**Hence, the slope and intercept of the line $2x-3y=12$ is slope $\left( m \right)=\dfrac{2}{3}$**

Intercept $\left( c \right)=-4$

Intercept $\left( c \right)=-4$

**Additional Information:**

Slope of a line is a number that describes both the direction and the steepness of the line. In the equation of a straight line when the equation written as $y=mx+c$ here the slope is the number $'m'$ that is multiplied on the $x.$ is the intercept that is the point where the line crossed axes. The useful form of the line equation is sensible named the “Slope-intercept form”

In the equation if the indignation is given then use $m=\tan \theta $ to find the slope and use the formula to get the equation.

**Note:**To find the slope and intercept you have to remember the general equation for comparing the given equation. Be careful while rearranging the equation. So, that you will not make mistakes and get the required solution.

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