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Choose the equation of the line passing through the point(-1,-2) and perpendicular to y= 1/4x + 2

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2 Answers

In the equation, 

y = 1/4x + 2, which is of the form y = mx+b,

m (the slope) = 1/4. Any parallel line will have the same slope, as you properly stated. A perpendicular slope is the negative inverse of the original (reciprocal with opposite sign). In this case it would be -4. 

The equation of our line is given as y=mx+b. In this case, our slope m is equal to 1/4 and our y intercept b is equal to 2.

Now, to find the line perpendicular to this first given line, our slope will have to be the negative reciprocal of the given slope. Our new slope for this line is then -1/(1/4) = -4.

To come up with an equation for this line, the problem has supplied us with a point that it must pass through. We have a handy point slope form equation that we can plug our information into to get an equation in the desired form.

Point Slope Form, for a slope m and given point (x1,y1) is given as:

y-y1 = m(x-x1)

Let's plug in our info. Our new slope is m = -4 and our point is (x1,y1)=(-1,-2)

y-(-2) = -4(x-(-1))

y+2 = -4(x+1)

y+2 = -4x-4

y = -4x-6 <-- answer

So if your answer choices are A, B, C, D - it would be choice B.