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
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.
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.