# GMAT Math : Calculating the slope of a perpendicular line

## Example Questions

### Example Question #1 : Calculating The Slope Of A Perpendicular Line

What is the slope of the line perpendicular to ?     Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, rewrite the equation in slope intercept form :   Slope of given line: Negative reciprocal: ### Example Question #2 : Calculating The Slope Of A Perpendicular Line

Line 1 is the line of the equation . Line 2 is perpendicular to this line. What is the slope of Line 2?      Explanation:

Rewrite in slope-intercept form:    The slope of the line is the coefficient of , which is . A line perpendicular to this has as its slope the opposite of the reciprocal of : ### Example Question #3 : Calculating The Slope Of A Perpendicular Line

Given: Calculate the slope of , a line perpendicular to .      Explanation:

To find the slope of a line perpendicular to a given line, simply take the opposite reciprocal of the slope of the given line.

Since f(x) is given in slope intercept form, .

Therefore our original slope is So our new slope becomes: ### Example Question #4 : Calculating The Slope Of A Perpendicular Line

What would be the slope of a line perpendicular to the following line?       Explanation:

The equation for a line in standard form is written as follows: Where is the slope of the line and is the y intercept. By definition, the slope of a line is the negative reciprocal of the slope of the line to which it is perpendicular. So if the given line has a slope of , the slope of any line perpendicular to it will have the negative reciprocal of that slope. This gives us:  ### Example Question #5 : Calculating The Slope Of A Perpendicular Line

What is the slope of a line perpendicular to the line of the equation ?    The line has an undefined slope.

The line has an undefined slope.

Explanation:

The graph of for any real number is a horizontal line. A line parallel to it is a vertical line, which has a slope that is undefined.

### Example Question #6 : Calculating The Slope Of A Perpendicular Line

Give the slope of a line on the coordinate plane.

Statement 1: The line shares an -intercept and its -intercept with the line of the equation .

Statement 2: The line is perpendicular to the line of the equation .

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. In order to determine the slope of a line on the coordinate plane, the coordinates of two of its points are needed. The -intercept of the line of the equation can be found by substituting and solving for :     The -intercept of the line is at the origin, . It follows that the -intercept is also at the origin. Therefore, Statement 1 only gives one point on the line, and its slope cannot be determined.

Assume Statement 2 alone. The slope of the line of the equation can be calculated by putting it in slope-intercept form :     The slope of this line is the coefficient of , which is . A line perpendicular to this one has as its slope the opposite of the reciprocal of , which is . 