Question

Find parametric equations for the curve with the given properties. The line with slope -2, passing through (-10,-20)

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asked 2021-03-29
Find parametric equations for the curve with the given properties.
The line with slope -2, passing through (-10,-20)

Answers (1)

2021-03-31
To find the parametric equation of the line with slope -2 passing through (-10,-20)
Given slope \(\displaystyle{m}={\frac{{\triangle{y}}}{{\triangle{x}}}}={\frac{{{y}_{{{s}}}}}{{{x}_{{{s}}}}}}=-{2}\)
\(\displaystyle\Rightarrow{x}_{{{s}}}={1},{y}_{{{s}}}=-{2}\)
Also \(\displaystyle{\left({x}_{{{1}}},{y}_{{{1}}}\right)}={\left(-{10},-{20}\right)}\)
The parametric equations of the line is given by
\(\displaystyle{x}={x}_{{{1}}}+{x}_{{{s}}}\cdot{t}\)
\(\displaystyle{y}={y}_{{{1}}}+{y}_{{{s}}}\cdot{t}\)
Substituting the values we have
\(\displaystyle{x}={x}_{{{1}}}+{x}_{{{s}}}\cdot{t}=-{10}+{1}{t}={t}-{10}\)
\(\displaystyle{y}={y}_{{{1}}}+{y}_{{{s}}}\cdot{t}=--{20}-{2}{t}=-{2}{t}-{20}\)
Hence x=t-10, y=-2t-20 are the required parametric equations.
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