Using point-slope form, write the equation of the line through (1, -5) and perpendicular to -3x+2y=12

Hello!

Remember that point slope form is written as: . In this form, m is the slope and and 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).

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: