The equation of the line which is parallel to the given line and passing through the given point is x + 2y + 2 = 0
It is an endless 1-dimension figure that has no width.
Given
Line x + 2y = 2
Point (2, -3)
Equation of parallel line is given by ax + by + c = 0
But the line is parallel to the given line x + 2y -2 = 0 so the coefficients of x and y will be the same.
a = 1
b = 2
Then line becomes x + 2y + c = 0
The line is passing through the point (2, -3)
[tex]\begin{aligned} 2 + 2(-3)+c &= 0 \\c &= 2 \\\end{aligned}[/tex]
Then the equation of the line which is parallel to the given line and passing through the given point is x + 2y + 2 = 0
Thus, the equation of the line which is parallel to the given line and passing through the given point is x + 2y + 2 = 0
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