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saveliy_v [14]
3 years ago
5

Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12

Mathematics
1 answer:
miskamm [114]3 years ago
3 0

keeping in mind that parallel lines have the same exact slope, hmmmm what's the slope of the line above anyway?

\bf 3y-x=-12\implies 3y=x-12\implies y=\cfrac{x-12}{3}\implies y = \cfrac{x}{3}-\cfrac{12}{3} \\\\\\ y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}

so we're really looking for the equation of a line whose slope is 1/3 and runs through (18,2)

\bf (\stackrel{x_1}{18}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{1}{3} \\\\\\ \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}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{18}) \\\\\\ y-2=\cfrac{1}{3}x-6\implies y=\cfrac{1}{3}x-4

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Step-by-step explanation:

\sf Answer \begin{cases}\sf \rightarrowtail \:( 3x - 6) + (2x + 25) + (x + 11) = 180 \\  \sf \rightarrowtail \: 3x - 6 + 2x + 25 + x + 11 = 180 \\  \sf \rightarrowtail \: 3x + 2x + x - 6 + 25 + 11 = 180 \\  \sf \rightarrowtail \: 6x + 30 = 180 \\  \sf \rightarrowtail \: 6x = 180 - 30 \\  \sf \rightarrowtail \: 6x = 150 \\  \sf \rightarrowtail \: x =  \frac{150}{6}  \\  \sf \rightarrowtail \: x = 25\end{cases}

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Step-by-step explanation:

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