Final answer:
The equation that represents a line going through the point (-5, 1) with a slope of -4/5 is y = -4/5x - 4.
Step-by-step explanation:
To find the equation of a line given a point and the slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values (-5, 1) for (x1, y1) and -4/5 for m, we get y - 1 = -4/5(x - (-5)).
Simplifying this equation gives us y - 1 = -4/5(x + 5), which can be rewritten as y = -4/5x - 4. Therefore, the equation that represents a line going through the point (-5, 1) with a slope of -4/5 is y = -4/5x - 4.