The equation of any straight line parallel to the straight line 2x – 3y + 6 = 0 can be written in the form 2x – 3y + c = 0, where c is the free term of the equation of the straight line.
Let us find at what value of the parameter c the straight line given by the equation 2x – 3y + c = 0 will pass through the point A (2; -4).
Substituting the values x = 2, y = -4 into the equation of the straight line, we get:
2 * 2 – 3 * (-4) + c = 0.
We find the value of c from this ratio:
4 – 12 + s = 0;
-8 + c = 0;
c = 8.
Therefore, the line given by the equation 2x – 3y + 8 = 0 will be parallel to the line 2x – 3y + 6 = 0 and will pass through the point A (2; -4).
Answer: the desired equation of the straight line 2x – 3y + 8 = 0.
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