A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]
where m represents the slope and b represents the y-intercept.
The line equation on our problem is written in standard form. The given line equation is
[tex]2x+3y=6[/tex]
To rewrite in slope intercept form, let's start by subtracting 2x from both sides:
[tex]\begin{gathered} 2x+3y-2x=6-2x \\ 3y=-2x+6 \end{gathered}[/tex]
Then, let's multiply both sides by 1/3:
[tex]\begin{gathered} \frac{1}{3}\cdot3y=\frac{1}{3}\cdot(-2x+6) \\ y=-\frac{2}{3}x+2 \end{gathered}[/tex]
Thus, this is our equation written in slope-intercept form
[tex]y=-\frac{2}{3}x+2[/tex]
