What is the equation of the line that is perpendicular to the line 3x+2y=8 and passes through the point (3,-7)

Answer 1

First we have to find the slope of the line perpendicular to 3x + 2y = 8, so we'll convert this equation to slope intercept form:

3x + 2y = 8

2y = 8 - 3x

y = -^3x/₂ +4

So the slope of this line is -³/₂

The slope of the perpendicular line is the negative reciprocal of this slope, so

m = -1/-3/2

m = ²/₃

Now we know the slope and one of the points the line passes through (3,-7) so we can write the equation as:

y+7 = ²/₃ (x-3)

or

y + 7 = ²/₃ x -2

y = ²/₃ x -9

Since the problem didn't say which type of equation to use, either one would be acceptable

Answer 2

The first thing you want to do is find the slope of the original equation.

Remember the relationship perpendicular lines have (their slopes are __________, _________).

Use the slope from the original equation to find the slope of the second line.

Plug the new slope and the point into the equation y=m(x-x₁)+y₁ (point-slope formula) where m is the slope, and the point (3,-7) is (x₁,y₁). Distribute m, then combine like terms.

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