Respuesta :

Answer:

[tex]\displaystyle y=-\frac{3}{2}x+b[/tex]

Step-by-step explanation:

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

[tex]\displaystyle 2y+3x=1\\\\2y=1-3x\\\\y=\frac{1}{2}-\frac{3}{2}x\\ \\y=-\frac{3}{2}x+\frac{1}{2}[/tex]

This tells us that since the slope of the line is [tex]\displaystyle -\frac{3}{2}[/tex], a line parallel to the given equation will also have a slope of [tex]\displaystyle -\frac{3}{2}[/tex], 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 [tex]\displaystyle y=-\frac{3}{2}x+b[/tex] where [tex]b[/tex] is a placeholder for any y-intercept, but [tex]\displaystyle b\neq\frac{1}{2}[/tex].

sqdancefan

Answer:

  2y +3x = 5

Step-by-step 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.

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