For this case we have that by definition, the standard form of the equation of the line is given by:
[tex]ax + by = c[/tex]
We have the following equation:
[tex]y-2 = - \frac {3} {2} (x + 6)[/tex]
We manipulate the equation algebraically:
[tex]y-2 = - \frac {3} {2} x- \frac {3 * 6} {2}\\y-2 = - \frac {3} {2} x \frac {18} {2}\\y-2 = - \frac {3} {2} x-9\\y-2 + 9 = - \frac {3} {2} x\\y-7 = - \frac {3} {2} x\\2 (y-7) = - 3x\\2y-14 = -3x\\3x + 2y = 14[/tex]
Finally, the equation is:
[tex]3x + 2y = 14[/tex]
Answer:
[tex]3x + 2y = 14[/tex]
