Final answer:
The equation of the line that passes through (-2, -7) and is perpendicular to y = -x + 7 is y = x - 5.
Step-by-step explanation:
To find the equation of a line that is perpendicular to y = -x + 7 and passes through (-2, -7), we first need to determine the slope of the given line. The equation y = -x + 7 is in the form y = mx + b, where m is the slope. In this case, the slope is -1.
The slope of a line perpendicular to this is the negative reciprocal of -1, which is 1.
Next, we'll use the slope and the point (-2, -7) to find the equation of the perpendicular line using the point-slope form. The formula is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values:
y - (-7) = 1(x - (-2))
y + 7 = x + 2
y = x - 5
Therefore, the equation of the line that passes through (-2, -7) and is perpendicular to y = -x + 7 is y = x - 5.