Finding the Equation of a Perpendicular Line Passing Through Two Points

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To find the equation of the perpendicular line S that passes through point A (3,4) and is perpendicular to line AB connecting points A (3,4) and B (7,-6), first calculate the gradient of AB, which is -2.5. The slope of line S, being perpendicular to AB, will be the negative reciprocal, resulting in a gradient of +2.5. Using the point-slope form of the equation with point A, the equation can be derived and rearranged into the standard form ax + by + c = 0. The relationship between the slopes of perpendicular lines is crucial for solving this problem. The final equation for line S can be determined from these calculations.
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equation of a line problem!

The points A and B have co-ordinates (3,4) and (7,-6) respectively. the straight line S passes through A and is perpendicular to AB.
FInd an equation for S, giving your answer in the form ax+by+c=0

Ok so I am really stuck on this question. So far i have calculated the gradient of the line AB by doing (-6-4)/(7-3) and i got -2.5

But now i don't know what to do please help :rolleyes:
 
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How are the slopes of perpendicular lines related?
 
i have no idea how the slopes are related
 
Two lines with gradients m and m' are perpendicular if (m)(m')=-1
 
so would that mean that my gradient is +2.5
 
Would it?

If m' x (-2.5) = -1, what does m' = ?
 

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