The equation of a line that passes through (0, 0) and is parallel to `3x+2y+8 = 0` must have the same slope as `3x + 2y + 8 = 0.`

Calculate the slope of line by rewriting in slope-intercept form: `(y=mx+b, m = slope)`

`3x + 2y + 8 = 0 rArr y= -3/2x - 4` Therefore slope is `-3/2`

**Therefore the equation passing through (0, 0) and slope of `-3/2` is:**

**`y = -3/2x + 0` **

**`y = -3/2x` **

**Written in standard form is: `3x + 2y = 0` **

The equation of the line passing through (0,0) and parallel to the the line 3x + 2y + 8 = 0 has to be determined.

The equation 3x + 2y + 8 = 0 can be written in the slope intercept form as y = (-3/2)x - 4. The slope of this line is -3/2. The slope of parallel lines is equal.

The equation of the required line is (y - 0)/(x - 0) = -3/2

=> 2y = -3x

=> 3x + 2y = 0

**The equation of the line passing through (0,0) and parallel to the line 3x + 2y + 8 = 0 is 3x + 2y = 0**

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