we are given the following equation:
[tex]3x+2y=12[/tex]
The slope-intercept form is the following:
[tex]y=mx+b[/tex]
Therefore, we need to solve for "y" in the equation. To do that we will subtract "3x" to both sides:
[tex]\begin{gathered} 3x-3x+2y=12-3x \\ 2y=12-3x \end{gathered}[/tex]
Now we will divide both sides by "2":
[tex]y=\frac{12-3x}{2}[/tex]
Now we will separate the numerator:
[tex]y=\frac{12}{2}-\frac{3}{2}x[/tex]
simplifying:
[tex]y=6-\frac{3}{2}x[/tex]
And thus we get the slope-intercept form.
