Question

Find the slope of a line perpendicular to the line whose equation is 6x + y = 8. Fully simplify your answer.

Answer 1

Answer: 1/6

Reason

6x + y = 8 solves to y = -6x+8

Compare that to y = mx+b

m = slope

b = y intercept

This tells us m = -6 is the slope. Think of it as -6/1. This is so we can flip the fraction and flip the sign to get 1/6 as the perpendicular slope.

-6 and 1/6 multiply to -1. This applies to any pair of slopes where neither line is vertical nor horizontal.

Answer 2

The slope of a line perpendicular to the line with the equation 6x + y = 8 is 1/6, obtained by taking the negative reciprocal of the original slope, which is -6.

Step-by-step explanation:

To find the slope of a line perpendicular to the given line, 6x + y = 8, we need to first find the slope of the given line. We can put the equation of the line into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with 6x + y = 8, we isolate y to get y = -6x + 8, which reveals that the slope of the given line is -6. To find the slope of a perpendicular line, we take the negative reciprocal of this slope. Since the negative reciprocal of -6 is 1/6, the slope of the line perpendicular to the given line is 1/6.