Find the equation of the line parallel to y equals 2 over 3 x plus 4 that passes through the point (2, 1) in slope-intercept form.


a.)
y equals short dash 3 over 2 x plus 7 over 2


b.)
y equals short dash 3 over 2 x plus 4


c.)
y equals 2 over 3 x minus 1 third


d.)
y equals 2 over 3 x minus 4 over 3



Answer :

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]