Hugh Soto

2022-09-13

Find the slope of a line that is perpendicular to V(3, 2), W(8, 5)

lloviznennj

Beginner2022-09-14Added 12 answers

The formula for find the slope of a line is:

$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$

Where $({{x}_{1}},{{y}_{1}})$ and $({{x}_{2}},{{y}_{2}})$ are two points on the line.

Substituting the values from the points in the problem gives:

$m=\frac{{5}-{2}}{{8}-{3}}=\frac{3}{5}$

Let's call the slope of a perpendicular line: ${m}_{p}$

The slope of a line perpendicular to a line with slope m is the negative inverse, or:

${m}_{p}}=-\frac{1}{{m}$

Substituting the slope for the line in the problem gives:

${m}_{p}}=\frac{-1}{{\frac{3}{5}}}=-\frac{5}{3$

$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$

Where $({{x}_{1}},{{y}_{1}})$ and $({{x}_{2}},{{y}_{2}})$ are two points on the line.

Substituting the values from the points in the problem gives:

$m=\frac{{5}-{2}}{{8}-{3}}=\frac{3}{5}$

Let's call the slope of a perpendicular line: ${m}_{p}$

The slope of a line perpendicular to a line with slope m is the negative inverse, or:

${m}_{p}}=-\frac{1}{{m}$

Substituting the slope for the line in the problem gives:

${m}_{p}}=\frac{-1}{{\frac{3}{5}}}=-\frac{5}{3$

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