Question

# If the lines $$y = 3x + 7$$ and $$2y + px = 3$$ are perpendicular to each other, find the value of $$p.$$

Solution

## Given line equations,$$y = 3x + 7$$Slope of this line $$= 3$$And,$$2y + px = 3$$$$2y = -px + 3$$$$y = (-p/2) + 3$$So, the slope of this line $$= -p/2$$For these two lines to be perpendicular to each other, the product of their slopes must be $$-1.$$$$(3) \times (-p/2) = -1$$$$3p/2 = 1$$$$p = 2/3$$Maths

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