Write an equation of the line that passes through (-5,2) and is perpendicular to y+3=2x

The gradient of a straight line that is perpendicular to y + 3 = 2x is -(1/2), as the gradient of the given line is +2.

 

So the equation of the perpendicular line is y = -(1/2)x + c, where c is a constant.  We can find the value of c because we know the line passes through (-5, 2), so at that point we must have:

2 = -(1/2)*(-5)+c

or

2 = 5/2 + c

so c = 2 - 5/2 

or c = -1/2

 

so the equation of the line becomes

y = -(1/2)x - (1/2)

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