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

[tex]\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}[/tex]

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

[tex]\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[/tex]

akposevictor

The equation in slope-intercept form of the line that passes through (18, 2) and is parallel to 3y - x = -12 is:

[tex]\mathbf{y = \frac{1}{3}x - 4}[/tex]

  • Recall that the slope of two lines that are parallel will always be the same.
  • Slope-intercept equation is y = mx + b (m = slope; b = y-intercept)

Therefore, given that a line is parallel to 3y - x = -2, and passes through,(18, 2)

  • Rewrite 3y - x = -2 in slope-intercept form.

Thus:

[tex]3y - x = -2\\\\3y = x - 2\\\\y = \frac{1}{3} x - \frac{2}{3}[/tex]

  • The slope of 3y - x = -2 is [tex]\frac{1}{3}[/tex].

Therefore, the slope (m) of the line that is parallel to 3y - x = -2 will be: m = [tex]\frac{1}{3}[/tex]

To find the y-intercept (b) of the parallel line, substitute (x, y) = (18, 2) and m = 1/3 into y = mx + b.

  • Thus:

[tex]2 = \frac{1}{3} (18) + b\\\\2 = 6 + b\\\\2 - 6 = b\\\\-4 = b\\\\b = -4[/tex]

Write the equation of the parallel line by substituting m = 1/3 and b = -4 into y = mx + b

  • Thus:

[tex]y = \frac{1}{3}x - 4[/tex]

Therefore, the equation in slope-intercept form of the line that passes through (18, 2) and is parallel to 3y - x = -12 is:

[tex]\mathbf{y = \frac{1}{3}x - 4}[/tex]

Learn more here:

https://brainly.com/question/12820056

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