Write the equation of a line parallel to 3x - y= -2 and passes through the point (0, -3).

The equation of a line parallel to 3x - y= -2 and passes through the point (0, -3) is     -3x + y + 3 = 0

Step-by-step explanation:

Here , the given equation of line 1 : 3x - y= -2

The Slope form of the equation is y = m x + c

⇒3x  + 2 =  y , where m  = 3 is the slope for the line 1

Now, as the Line 2 is parallel to Line 1,

Slope of Line 1 (m1)   = Slope of Line 1 (m2)

Hence, the slope of line 2 = 3

Now, by POINT SLOPE FORMULA

The equation of line with point (x0, y0) is given as

(y - y0) = m (x - x0)

⇒ For the point (0,-3) the equation of Line 2  is:

    y  - (-3)  = 3 ( x-0)

or,  y + 3 =  3x ⇒  -3x + y + 3 = 0

Hence, the equation of a line parallel to 3x - y= -2 and passes through the point (0, -3) is  -3x + y + 3 = 0

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