Final answer:
The equation of the line that passes through the point (5,7) with a slope of -1 is y = -x + 12.
Step-by-step explanation:
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope of the line.
In this case, the point is (5,7) and the slope is -1. Plugging in these values into the point-slope form, we have:
y - 7 = -1(x - 5)
Simplifying, we get:
y - 7 = -x + 5
y = -x + 5 + 7
y = -x + 12
Therefore, the equation of the line that passes through the point (5,7) with a slope of -1 is y = -x + 12.