Answer:
y + 4 = -12(x - 4)
Explanation:
Relationship between the slopes of parallel lines and finding the slope of the other line:
- The slopes of parallel lines are the same, meaning finding the slope of y - 1 = -12(x + 5) will allow us to find the slope of the other line.
y - 1 = -12(x +5) is in the point-slope form of a line, whose general equation is given by:
y - y1 = m(x - x1), where
- (x1, y1) is any point on the line,
- and m is the slope.
Thus, the slope of both the other line and y - y1 = -12(x + 5) is -12.
Writing the equation of the other line:
- We know that the slope of the other line is -12 and that it passes through the point (4, -4).
Now we can find the equation of the other line in point-slope form by substituting -12 for m and (4, -4) for (x1, y1):
y - (-4) = -12(x - 4)
y + 4 = -12(x - 4)
Therefore, y + 4 = -12(x - 4) is the equation of the line (in point-slope form) that passes through the point (4, -4) and it parallel to the line with the equation y - 1 = -12(x + 5).