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Answer:
[tex]\textsf{c)} \quad y=\dfrac{2}{3}x-\dfrac{1}{3}[/tex]
Step-by-step explanation:
The slope-intercept form of a linear equation is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope-intercept form of a linear equation}}\\\\y=mx+b\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\;\textsf{$b$ is the $y$-intercept.}\\\end{array}}[/tex]
Given linear equation:
[tex]y=\dfrac{2}{3}x+4[/tex]
Therefore, the slope of the given equation is m = 2/3 and the y-intercept is b = 4.
Parallel lines are lines in a plane that never intersect and are always the same distance apart. For two lines to be parallel, they must have the same slope. Therefore, the slope of a line parallel to y = 2/3 x + 4 is:
[tex]m=\dfrac{2}{3}[/tex]
To find the equation of the line parallel to y = 2/3 x + 4 that passes through the point (2, 1) in slope-intercept form, substitute m = 2/3, x = 2 and y = 1 into the slope-intercept formula and solve for b:
[tex]1=\dfrac{2}{3}(2)+b \\\\\\ 1=\dfrac{4}{3}+b \\\\\\ b=1-\dfrac{4}{3}\\\\\\b=-\dfrac{1}{3}[/tex]
Therefore, the equation of the parallel line is:
[tex]\Large\boxed{\boxed{y=\dfrac{2}{3}x-\dfrac{1}{3}}}[/tex]