Line k is defined as y = -5/7 + 6. Line j is perpendicular to line k. What is the slope of line j?

Answer 1

Your equation appears to be incorrect, but you can remember that: the slope of [line J] perpendicular to any [line K] is the negative reciprocal of the slope of [line K].

Answer 2

Problem

Given the equation K = -(5/7)x + 6, find the equation of line J perpendicular to line K.

Step 1

Recall that in order for a line to be perpendicular to another line, the slope of both lines must be opposite; that is, if the slope of a line is 2, then its perpendicular correspondent would have a slope of -½. Similarly, parallel lines will have the same slope as each other.

A good mnemonic device to remember this property is "flip and switch" - flip the fraction over and switch the sign.

Step 2

Since we have a slope of -5/7 for line K, line J must have a slope of 7/5 (the opposite of line K); therefore, the equation of line J is J = (7/5)x + 6.

Solution

The equation for line J is y = (7/5)x + 6.

Answer 3

AIn order to find a line that is perpendicular to a given equation, the perpendicular line will have a slope that is a negative reciprocal to the given slope.

A reciprocal of a number is what you multiply it by to get 1. A negative reciprocal of a number is what you multiply it by to get -1.

In this case, the negative reciprocal of the given slope -5/7 is 7/5.

An easy way to remember how to do the negative reciprocal is to change the sign and flip the numbers. If the original slope is positive, the negative reciprocal would then be negative and vice versa.

Answer 4

y = (-5/7)x + 6

A line perpendicular to it will have a slop that's 7/5.

Flip the slope. Change the sign.

Slope of j = 7/5.

Answer 5