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

Perpendicular slope: -7x

Parallel slope: 1/7x

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

`\displaystyle \parallel\:(1)/(7) \\ \perp\:-7`

Explanation:

`\displaystyle x - 7y = 1 \hookrightarrow (-7y)/(-7) = (-x + 1)/(-7) \\ \\ \boxed{y = (1)/(7)x - (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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