Final answer:
The point-slope form of the line that has the same slope as y = -1/2x + 7 and contains the point (4, -5) is y + 5 = (-1/2)(x - 4).
Step-by-step explanation:
To write the equation in the point-slope form of the line that has the same slope as the line y = -1/2x + 7 and contains the point (4, -5), we should start by identifying the slope of the given line. Since the given line is in the form y = mx + b, where m represents the slope, the slope (m) is -1/2.
Now, the point-slope form of an equation of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the point (4, -5) and the slope -1/2, we get:
y - (-5) = (-1/2)(x - 4)
Simplifying, we have:
y + 5 = (-1/2)(x - 4)
This is the equation of the line in point-slope form with the given slope and passing through the specified point.