Find the Perpendicular Line 3x+5y-8=0 , (-8,1)

Problem

3*x+5*y−8=0,(−8,1)

Solution

1. Rewrite the given equation in slope-intercept form y=m*x+b to identify the slope of the original line.

3*x+5*y−8=0

5*y=−3*x+8

y=−3/5*x+8/5

2. Identify the slope of the original line, which is (m_1)=−3/5

3. Determine the slope of the perpendicular line by taking the negative reciprocal of (m_1)

(m_2)=−1/(m_1)

(m_2)=5/3

4. Apply the point-slope formula y−(y_1)=m*(x−(x_1)) using the point (−8,1) and the new slope (m_2)=5/3

y−1=5/3*(x−(−8))

y−1=5/3*(x+8)

5. Simplify the equation into slope-intercept form.

y−1=5/3*x+40/3

y=5/3*x+40/3+1

y=5/3*x+43/3

6. Convert to general form A*x+B*y+C=0 if required.

3*y=5*x+43

5*x−3*y+43=0

Final Answer

y=5/3*x+43/3

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