Let's rewrite the equation of the line in the form y = mx + b.
6x - 12 = 4y
[tex] \frac{3x}{2} - 3 = y[/tex]
Since [tex]m_t = \frac{3}{2}[/tex],
[tex]m_n = \frac{-2}{3}[/tex]
Now, we have a point and a slope, so we'd just substitute everything to the point-gradient form.
[tex]y - \frac{3}{2} = \frac{-2}{3}(x - 3)[/tex]
[tex]3y - \frac{9}{2} = -2(x - 3)[/tex]
[tex]3y - \frac{9}{2} = -2x + 6[/tex]
[tex]2x + 3y - \frac{9}{2} - 6 = 0[/tex]
[tex]2x + 3y - \frac{21}{2} = 0[/tex]
[tex]4x + 6y - 21 = 0[/tex]
[tex]6y = 21 - 4x[/tex]
[tex]y = -\frac{2x}{3} + \frac{7}{2}[/tex]
