How do you write $2x+3y=6,$ in slope intercept form.

Hint: Rewrite the given equation in form of general equation of slope intercept form, i.e. $y=mx+c,$ then compare the obtained equation with general equation and determine the value of $'m'$ i.e. gradient of line or slope of line and $'c'$ then draw the graph of equation.

Complete step by step solution:
As per data given in the question,
Here we have,
$2x+3y=6$
As, we have to represent the above equation in slope intercept form.
We know that,
In slope intercept form,
Any equation is represented in form of $y=mx+c$
So, representing the given equation in form of general equation of slope intercept form,
We will get,
$2x+3y=6$
$\Rightarrow 3y=-2x+6$
$\Rightarrow y=\dfrac{-2x+6}{3}$
Now converting the obtained equation, we will get,
$y=\dfrac{-2x}{3}+\dfrac{6}{3}$
$\Rightarrow y=\dfrac{-2}{3}x+2...(i)$
Comparing equation $(i)$ with general equation of slope intercept form,
We will get,

Value of $m=\dfrac{-2}{3}$ hence, we can say that line have a gradient of $\dfrac{-2}{3}$ value of $'c'$value of $y$ intercept is $2$ means the line cuts $y$-axis at $2.$

Note: Always represent the given equation in the form of a general slope. Intercept form
i.e. $y=mx+c,$
$m$ is called the gradient of line.
While representing the equation in $y=mx+c,$ do not ignore the sign of $'m'$ as $m$ can be positive or negative.