The equation of the line that is parallel to the given line and passes through the point (2, 3) is,
[tex]x+2y=8[/tex]
The equation of the line is the way of representation of a line in the equation form.
The equitation of the lines represents the line by the set of points on which the line lies or passes through in the coordinate system.
Given information-
The points through which the line passes is (2, 3).
The points of the line shown in the image attached below is (-4, 0) and (4, -4).
The slope of the line shown in the image which passes through the point (-4, 0) and (4, -4) is,
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{-4-0}{4-(-4)}\\m=\dfrac{-4}{8}\\m=\dfrac{-1}{2}[/tex]
As the line which passes through the point (2, 3) is parallel to the line shown below. Hence, the slope of it must be equal to that line.
Therefore the equation of the line which passes through the point (2, 3) and has a slope of -1/2, is,
[tex](y-y_1)=m(x-x_1)\\(y-3)=-\dfrac{1}{2}(x-2)\\2(y-3)=-x+2\\2y-6=-x+2\\x+2y=8[/tex]
Thus the equation of the line that is parallel to the given line and passes through the point (2, 3) is,
[tex]x+2y=8[/tex]
Hence, the option 2 is the correct option.
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