Question

Write the equation of a line which is
parallel to 2y + 3x = 1​

Answer 1

`\displaystyle y=-(3)/(2)x+b`

Explanation:

A line parallel to the given equation will have the same slope, so if we convert the equation to slope-intercept form:

`\displaystyle 2y+3x=1\\\\2y=1-3x\\\\y=(1)/(2)-(3)/(2)x\\ \\y=-(3)/(2)x+(1)/(2)`

This tells us that since the slope of the line is
`\displaystyle -(3)/(2)`, a line parallel to the given equation will also have a slope of
`\displaystyle -(3)/(2)`, but must have different y-intercepts (otherwise they are the same line obviously and won't be parallel).

So, the equation form of a parallel line would be
`\displaystyle y=-(3)/(2)x+b` where
`b` is a placeholder for any y-intercept, but
`\displaystyle b\\eq(1)/(2)`.

Answer 2

2y +3x = 5

Explanation:

Any line in the same form with the same coefficients of x and y will be parallel to the given line:

2y +3x = c . . . . . for any suitable constant c

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Additional comment

The value of c can be chosen so the line passes through a point of your choice. For example, if you want the line to go through the point (1, 1), then the value of c will be ...

2(1) +3(1) = c = 5

Line 2y +3x = 5 is parallel to 2y +3x = 1 and will go through point (1, 1).

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The slope is determined by the ratio of the x- and y-coefficients. The position of the line on the coordinate plane is determined by the constant. Any line with the same slope will be parallel to the given line.