GMAT Math Practice - Coordinate Geometry

GMAT Math Practice - Coordinate Geometry 

Question

Line P is described by the equation 3x + 2y - 4 = 0.  Which of the following lines is parallel to P and has the same x-intercept as the line  5x - y + 5 = 0?
a) 6x = -5y + 20
b) -y = (3/2)x +20
c)  -4x - 6y =8
d)  y = -3x - 3
e) - 4y = -6x-12

Solution

 For some reason, many GMAT test takers seem to be confused with such a question and they immediately start by plotting points on the axes.

 You need to know simple rule for parallel lines.

Lines are parallel when they have the same slopes, and the slope is easiest to see when a line is written in slope intercept from y = mx + b.

Converting P to that form we get
y = -3x + 4 or
y = -3x + 4
So the slope of any parallel line will be -3. The second condition is given by the 2nd equation.  Its x-intercept is the x-value where y = 0.

That is 5x - 0 + 5 = 0
5x = -1 so
x = -1 .

For each of the given answer choices, we can start by looking for either a matching slope or x-intercept, and then if it matches one, see if it matches both.

Answer D is y = -3 x - 3.

y = -(3)x -3

Therefore the slope is -3, and parallel to P.  Furthermore, substituting in x = -1.y = -3 x -3

y = 3 - 3 = 0 

So this line also has the desired x intercept.