The liner equation 2x+5+6x=2/3(5x-3) is given. A. Solve the liner equation: X =
B. Check that the solution is correct.

Solved

Show answers

Ответ:

zitterkoph

25.07.2022

Mathematics

bearing in mind that perpendicular lines have negative reciprocal slopes.

$\bf y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{2}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{2}}\qquad \stackrel{negative~reciprocal}{\cfrac{3}{2}}}$

so we're really looking for the equation of a line whose slope is 3/2 and runs through (-4,13)

$\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{13})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{\cfrac{3}{2}}[x-\stackrel{x_1}{(-4)}] \\\\\\ y-13=\cfrac{3}{2}(x+4)\implies y-13=\cfrac{3}{2}x+6\implies y=\cfrac{3}{2}x+19$

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice

The liner equation 2x+5+6x=2/3(5x-3) is given. A. Solve the liner equation: X =B. Check that the solution is correct. ​