Which of the following lines is perpendicular to y = − 2x + 3 and has

Hi All,

This question is based on a pair of graphing/line rules that you might not actually use on Test Day (but they're good to know since they're part of the broader group of line rules that come with Co-ordinate Geometry).

We're asked which of the following lines is PERPENDICULAR to y = − 2x + 3 and has the same Y-INTERCEPT as y = 2x − 3.

The second piece of information is easier to deal with, so we'll start there. Both of the given equations are written in slope-intercept 'format', which is helpful:

Slope-intercept: Y = MX + B, where M is the slope and B is the Y-intercept of the line.

Since the second equation has a y-intercept of -3, the line we're looking for ALSO has a y-intercept of -3.
Eliminate Answers A, C and D.

Perpendicular lines criss-cross one another and form 90 degree angles. The lines have "opposite inverse" slopes (sometimes called "negative reciprocal" slopes). The line that we're given has a slope of -2, so the "opposite inverse" line would have a slope of +1/2.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

This question tests your knowledge about the various terms used in coordinate geometry.

If two lines are perpendicular, then the product of their slopes will be = -1

How to find the slope:
Any line can be written in the form y = mx + c
Where m is the slope and c is the intercept.

In this case, slope of y = -2x + 3 is "-2"

Hence the answer choice should have the slope as "1/2"
Only options B and C remain.

Next we need the intercept to be same.
The intercept given is "-3"
Hence the equation of the line will be y = 1/2*x - 3

Option B

Recall that the slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the value of its y-intercept. We see that the line y = -2x + 3 has a slope of -2 and the line y = 2x - 3 has a y-intercept of -3.

Since the slopes of perpendicular lines are negative reciprocals of each other, the slope of the line that is perpendicular to a line with slope of -2 is 1/2. We also see that the line needs to have a y-intercept of 3; thus, the equation of that line is:

y = (1/2)x - 3

Answer: B

Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?

Two lines are said to be parallel if the multiplication of their slope is \(= -1\)

Given Line has a Slope = -2

Hence, we are looking for slope of \(\frac{1}{2}\) as \(\frac{1}{2} * -2 = -1\)

And y intercept of the second like = -1

Hence, Line with Slope \(\frac{1}{2}\) and Y Intercept \(= -3\) is line B

\(y = \frac{1}{2}*x - 3\)

Hence, Answer is B

For this question i went through the options. The slope of a line is -2 and the slope of the perpendicular line is 1/2 because the product of the 2 slopes must be -1(-2*1/2). So the options B and C only can be considered. Now since the y intercept must be (0,-3) only option B must be considered. Am i correct in my concept . Kindly help. Thanks

Slope of y = -2x+3 is -2
slope of line perpendicular to this line = 1/2
Line perpendicular to y = -2x+3 is y = 1/2*x + m where is m is intercept on y -axis

y-intercept of y = 2x -3 is -3

So, the desired equation becomes y = 1/2*x -3

Answer B

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