Final answer:
The equation of the tangent line to the curve y = 3 - 5x at the point (-1, 8) is y = -5x + 3.
Step-by-step explanation:
To find the equation of the tangent line to the curve y = 3 - 5x at the point (-1, 8), we need to determine the slope of the tangent line. For a linear equation like y = 3 - 5x, the slope is the coefficient of x, which in this case is -5. Knowing that a tangent to a curve at a given point has the same slope as the curve at that point, we can use the point-slope form of a line equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point of tangency.
Substituting the given point (-1, 8) and the slope -5 into the equation, we get y - 8 = -5(x + 1). Simplifying this equation, we get y - 8 = -5x - 5. Finally, adding 8 to both sides to solve for y gives us the equation of the tangent line: y = -5x + 3.