Hello!
Remember that point slope form is written as: [tex]y - y_{1} = m(x - x_{1})[/tex]. In this form, m is the slope and [tex]x_{1}[/tex] and [tex]y_{1}[/tex] is a given ordered pair.
Before finding the perpendicular line, we need to change the given equation to slope-intercept form, which is give us the slope.
-3x + 2y = 12 (add 3x to both sides)
2y = 12 + 3x (divide both sides by 2)
y = 3/2x + 6 | The slope of the original equation is m = 3/2.
With the slope, we can change it to become a perpendicular line. We need to find the "negative reciprocal" of the slope of the given line. It is also written as -1/m.
-1/(2/3) → -3/2 | The slope of perpendicular line is -3/2.
Now, we substitute the slope into the point-slope form, and also the given ordered pair.
Therefore, the final answer is: y + 5 = -3/2(x - 1).
