SOLUTION: Perpendicular Lines: Write the equation of the line through (4,5) and perpendicular to the line with equation 3x + 2y = -1. Please explain how the equation came out to y = 2/3 x

Question 260757: Perpendicular Lines: Write the equation of the line through (4,5) and perpendicular to the line with equation 3x + 2y = -1.
Please explain how the equation came out to y = 2/3 x + 7 as shown in my example answer key.
Thank you,
Melissa
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, we must solve for y to get the equation in slope intercept form.

Start with the given equation

Subtract 3x from both sides.

Rearrange the terms.

Divide both sides by 2 to isolate y.

Break up the fraction and simplify.

So the equation is now in slope intercept form where the slope is and the y intercept is

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Recall that perpendicular lines have slopes that are negative reciprocals of one another. So because the slope of the given line is , the perpendicular slope is (just flip the fraction and change the sign).

So we now know that the slope of the perpendicular line is and it goes through the point (4,5).

Now let's use the point-slope formula to find the perpendicular equation.

Start with the point-slope formula

Plug in

Plug in and . This is given from (4,5). Our goal now is to solve for y.

Distribute

Multiply

Add 5 to both sides.

Combine like terms.

So the equation of the perpendicular line is (make sure that there isn't a typo). Notice that if we graph the two lines, we get

Graph of (red) and (green) going through the point (4,5). Notice how the red line is perpendicular to the green line.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Glad you provided the answer you have.
First we have to find the slope of the given line
3x+2y=-1
Get y by itself
2y=-3x-1
y=-3x/2-1/2
The slope is -3/2
So the perpendicular line has to have a slope of 2/3
2/3*(-3/2)=-1
The new line goes through (4,5)
Plug in 4 and 5 to find b
5=2*4/3+b
15/3-8/3=b
7/3=b
y=2x/3+7/3
or 3y=2x+7

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