Find the slope perpendicular to x+2y=7

Colten Andrade
2022-09-26
Answered

Find the slope perpendicular to x+2y=7

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Nancy Phillips

Answered 2022-09-27
Author has **12** answers

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the equation of a line in slope-intercept form is.

y=mx+b

where m is the slope and b the y-intercept

rearrange x+2y=7 into this form

subtract x from both sides

2y=−x+7

divide all terms by 2

$y=-\frac{1}{2}x+\frac{7}{2}\leftarrow \text{in slope-intercept form}$

$\text{with slope m}\phantom{\rule{1ex}{0ex}}=-\frac{1}{2}\text{}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}b=\frac{7}{2}$

given a line with slope m then the slope of a line perpendicular to it is

$\u2022{x}{m}_{\text{perpendicular}}}=-\frac{1}{m$

$m}_{\text{perpendicular}}=-\frac{1}{-\frac{1}{2}}=2\leftarrow \text{perpendicular slope$

y=mx+b

where m is the slope and b the y-intercept

rearrange x+2y=7 into this form

subtract x from both sides

2y=−x+7

divide all terms by 2

$y=-\frac{1}{2}x+\frac{7}{2}\leftarrow \text{in slope-intercept form}$

$\text{with slope m}\phantom{\rule{1ex}{0ex}}=-\frac{1}{2}\text{}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}b=\frac{7}{2}$

given a line with slope m then the slope of a line perpendicular to it is

$\u2022{x}{m}_{\text{perpendicular}}}=-\frac{1}{m$

$m}_{\text{perpendicular}}=-\frac{1}{-\frac{1}{2}}=2\leftarrow \text{perpendicular slope$

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I want to normalize these so that any two equations that represent the same line can be compared programatically to see if they're equal just using the co-efficients. For this I need the co-efficients of any two equations representing the same line to be equivalent after normalizing.

I normalized the values by dividing all coefficients by

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