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pav-90 [236]
3 years ago
9

Find the equation of a line that passes through (-2,4) and (1,-2)

Mathematics
1 answer:
Basile [38]3 years ago
8 0

\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-6}{1+2}\implies \cfrac{-6}{3}\implies -2

\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-2}[x-\stackrel{x_1}{(-2)}]\implies y-4=-2(x+2) \\\\\\ y-4=-2x-4\implies y = -2x

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<em><u>To </u></em><em><u>find:</u></em>

<em><u>=</u></em><em><u>></u></em><em><u> </u></em><em><u>The</u></em><em><u> </u></em><em><u>value</u></em><em><u> of</u></em><em><u> </u></em><em><u>x</u></em>

<em><u>=</u></em><em><u>></u></em>

<em><u>x - 8 =  - 11</u></em>

<em><u>Now,</u></em><em><u> we'll</u></em><em><u> </u></em><em><u>move </u></em><em><u>-</u></em><em><u>8</u></em><em><u> </u></em><em><u>to </u></em><em><u>the</u></em><em><u> </u></em><em><u>other</u></em><em><u> </u></em><em><u>side </u></em><em><u>i.e </u></em><em><u>the </u></em><em><u>RHS </u></em><em><u>side,</u></em>

<em><u>which</u></em><em><u> </u></em><em><u>results</u></em><em><u> </u></em><em><u>in </u></em><em><u>the </u></em><em><u>change</u></em><em><u> </u></em><em><u>of </u></em><em><u>it's</u></em><em><u> </u></em><em><u>sign(</u></em><em><u>-</u></em><em><u> </u></em><em><u>converts</u></em><em><u> </u></em><em><u>into </u></em><em><u>+</u></em><em><u>)</u></em>

<em><u>=</u></em><em><u>></u></em>

<em><u>x =  - 11 + 8</u></em>

<em><u>Now </u></em><em><u>,</u></em><em><u> we'll</u></em><em><u> </u></em><em><u>add </u></em><em><u>the </u></em><em><u>Numbers</u></em>

<em><u>=</u></em><em><u>></u></em>

<em><u>x =   - 3</u></em>

<h2><em><u>Hence</u></em><em><u>,</u></em><em><u>-</u></em><em><u>3</u></em><em><u> </u></em><em><u>is </u></em><em><u>the</u></em><em><u> </u></em><em><u>required</u></em><em><u> </u></em><em><u>answer</u></em><em><u>.</u></em></h2>

<em><u>^</u></em><em><u>-</u></em><em><u>^</u></em>

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