Which of the following equations represents a line

Hi All,

We're asked for a line that is PERPENDICULAR to Line K in the figure above. This question is based on 'line rules' and requires a bit of Arithmetic to solve.

Perpendicular lines have an 'opposite inverse' (re: "negative reciprocal") slope. For example, if one line has a slope of 3, then a perpendicular line to that first line would have a slope of -1/3. As such, we have to find the slope of Line K first - and then we'll know the slope of the perpendicular line that we're looking for.

From the drawing, we can see that Line K hits points (0, -6) and (12, 0), so it has a slope of +6/12 = +1/2. Thus, the perpendicular line that we're looking for has a slope of -2.

The simplest version of that type of line would be Y = -2X. You'll notice that none of the answer choices are written in that format... but if we add "2X" to both sides, we would have an equation that included Y + 2X..... and we do have one answer in that format. Since that equation has no other variables (it's Y + 2X = 12)... that line has a slope of -2, so it must be the answer.

Final Answer: D

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Which of the following equations represents a line perpendicular to line k in the figure above?

A. 3x + 2y = -12
B. 2y + x = 0
C. 2y - x = 0
D. y + 2x = 12
E. y - 2x = 12

OA D

We see that the slope of line k is (0 - (-6))/(12 - 0) = 6/12 = 1/2. Therefore, the slope of a line perpendicular to line k is -1/(1/2) = -2. Looking at the given answer choices, we see that choice D (y + 2x = 12) has a slope of -2 since the equation, in slope-intercept form, is: y = -2x + 12.

Answer: D