Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We are given a line with a positive slope (i.e., sloping upward from left to right) that intersects the x-axis at point (-3,0) and at the y-axis at (0,2). With this information we can determine the equation of the line. Let’s start by calculating the slope.
Slope = (change in y)/(change in x) = (2-0)/(0-(-3)) = 2/3
We also see that the y-intercept is 2. Using the slope-intercept form of a line, y = mx + b, we determine that the equation of our line is:
y = (2/3)x + 2
We need to determine which answer choice has a slope that is equal to the slope of line L. (Remember that parallel lines have the same slope.) In other words, we must find an answer choice such that the slope of the line is 2/3.
However, rather than manipulating each answer choice, we are going to manipulate the equation y = (2/3)x + 2 to look more like our answer choices.
y = (2/3)x + 2
Multiplying our equation by 3 gives us:
3y = 2x + 6
3y – 2x = 6
We see that only answer choice A has “3y – 2x” and this is enough information to determine that the line in answer choice A also has a slope of 2/3.
If we want to be absolutely sure, we can manipulate the equation in answer choice A and isolate y to determine the slope.
3y – 2x = 0
3y = 2x
y = (2/3)x
We see that the slope is indeed 2/3.
Answer: A
