Final answer:
The slope-intercept form of the equation of the line is y = -4x - 3.
Step-by-step explanation:
The slope-intercept form of the equation of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the line passes through the point (-2, 5) and has a slope of -4, we can substitute these values into the equation to find the specific equation of the line.
Using the point-slope form of a line, we have: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the values (-2, 5) and -4 into the equation, we get:
y - 5 = -4(x - (-2))
Simplifying further, we have:
y - 5 = -4(x + 2)
Expanding the brackets, we get: y - 5 = -4x - 8
Finally, rearranging the equation to the slope-intercept form, we have: y = -4x - 3