Answer: 5x - 2y = -2
To find the equation of the line, we need to determine its slope. Since the line we want to find is parallel to the given line, it has the same slope as the given line.
To find the slope of the given line, we can rearrange it into slope-intercept form:
5x - 2y = 6
-2y = -5x + 6
y = (5/2)x - 3
So the slope of the given line is 5/2.
Now we can use the point-slope form of a line to write the equation of the line we want to find:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (-2, -4) we want the line to pass through.
Substituting m = 5/2, x1 = -2, and y1 = -4, we get:
y - (-4) = (5/2)(x - (-2))
y + 4 = (5/2)(x + 2)
Multiplying both sides by 2 to eliminate the fraction, we get:
2y + 8 = 5x + 10
Subtracting 5x and 8 from both sides, we obtain the final form of the equation:
5x - 2y = -2