In the x-y plane, line l is perpendicular to line k. If the equation of line k is 3x – 7y = 21, what is the equation of line l if contains the point (0, 4)?

(A) 3x + 7y = 4

(B) 7x – 3y = 12

(C) 7x + 3y = 4

(D) 7x + 3y = 12

(E) 7x + 3y = 28

Correct Answer : Choice D. 7x + 3y = 12

Explanatory Answer

Equation of line k is 3x – 7y = 21.

Let us express the equation of line k in the standard form as y = (3/7)x – 3.

The slope of line k is 3/7.

Line l is perpendicular to line k.

The product of the slopes of two perpendicular lines is -1.

So, if m is the slope of line l, then m*(3/7) = -1

or m = -7/3.

Equation of a line whose slope is m and whose y-intercept is c is y = mx + c.

Line l passes through the point (0, 4).

So, line l intercepts the y-axis as 4.

Hence, its equation is y = (-7/3)x + 4

Or 3y = -7x + 12

Or 7x + 3y = 12.

oleg says

In this particular question, since the x-coordinate is zero and all the numbers are small integers, it is more efficient to first check which of the lines among A-E contain the point (0,4). As it turns out only line (D) passes through (0,4) and hence the only possible answer.