Final answer:
In this case, the equation of a line with a given slope that passes through a point is y = -5x - 1.
Step-by-step explanation:
To find the equation of a line with a given slope that passes through a point, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
In this case, the slope is -5 and the point is (1, -6), so the equation is:
y - (-6) = -5(x - 1).
Simplifying this equation, we get :
y + 6 = -5x + 5.
Finally, rearranging the equation, we have y = -5x - 1.