Question

Consider the line x-7y=1
What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line?

Answer 1

Answer:

Perpendicular slope: -7x

Parallel slope: 1/7x

Step-by-step explanation:

Rewrite this into slope-intercept form. So y=1/7x -1/7

Slope of a perpendicular line is the reciprocal of the original slope. So perpendicular line would be y=(-7)x-1/7. Slope in the perpendicular is -7. A parallel line will have the same slope,so basically y=1/7x-1 .

It doesn't matter what the y-int would be since a perpendicular/parallel slope only depends on the slope itself.

Answer 2

Answer:

$\displaystyle \parallel\:\frac{1}{7} \\ \perp\:-7$

Step-by-step explanation:

$\displaystyle x - 7y = 1 \hookrightarrow \frac{-7y}{-7} = \frac{-x + 1}{-7} \\ \\ \boxed{y = \frac{1}{7}x - \frac{1}{7}}$

Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so ⅐ remains as is. Perpendicular equations however, have OPPOCITE MULTIPLICATIVE INVERCE RATE OF CHANGES, so ⅐ becomes −7.

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