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Question 1: Find the equation of the line through point (5,4) and perpendicular to y=−43x−2. Use a forward slash (i.e. "/") for fractions (e.g. 1/2. Question 2:Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6. Use a forward slash (i.e. "/") for fractions (e.g. 1/2.

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Answer:

Question 1: y = 3/4x + 1/4.

Question 2: y = 6/5x + 7/5.

Step-by-step explanation:

Question 1: A line perpendicular to another line would have a slope that is the negative reciprocal of the other line. If the slope of the first line is -4/3, the slope of a line perpendicular to the first would have a slope of 3/4.

Since the line goes through (5, 4), we can just put the points into the equation, y = 3/4x + b.

4 = 3/4(5) + b

b + 15/4 = 4

b = 16/4 - 15/4

b = 1/4

So, the equation of the line is y = 3/4x + 1/4.

Question 2: 5x + 6y = -6

6y = -5x - 6

y = -5/6x - 1

As stated before, a line perpendicular to another will have a slope that is the negative reciprocal of the other. So, the slope of the other line is 6/5.

The line goes through (-2, -1), so we can put the points into the equation, y = 6/5x + b.

-1 = 6/5(-2) + b

b - 12/5 = -5/5

b = -5/5 + 12/5

b = 7/5

So, the equation of the line is y = 6/5x + 7/5.

Hope this helps!

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