Question

Which choice is the equation of a line that passes through the point (–6, –2) and is perpendicular to the line represented by this equation?
y = −3x + 1

A. 3x + y = 1
B. y = 1/3x
C. y = −3x
D. −3y = −x + 1

Answer 1

Answer:

  B.  y = 1/3x

Step-by-step explanation:

The slope of the given line is -3, so the slope of the perpendicular line will be the negative reciprocal of that: -1/(-3) = 1/3. This eliminates choices A and C.

We can find the y-intercept (b) if we use the given point values in the equation ...

  y = 1/3x +b

we get ...

  -2 = (1/3)(-6) +b

  -2 = -2 +b . . . simplify

  0 = b . . . . . . . add 2

So, the equation of the perpendicular line through the given point is ...

  y = 1/3x . . . . matches choice B

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Alternate solution method

You can try the given point in the given equations. You will find that only the equation of choice B will work.