Final answer:
The equation of the line perpendicular to the line y - 4 = 5/2(x - 2) that passes through the point (-1, -4) is y = -2/5x - 14/5.
Step-by-step explanation:
The equation of a line that is perpendicular to another line can be found by taking the negative reciprocal of the original line's slope.
In this case, the line y - 4 = 5/2(x - 2) has a slope of 5/2.
The slope of the perpendicular line would then be the negative reciprocal, which is -2/5.
Next, we use the point-slope form of a line's equation, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is the given point through which the line passes.
Plugging in the slope -2/5 and the point (-1, -4) into this form gives us the perpendicular line's equation:
y + 4 = -2/5(x + 1)
Finally, to convert this into slope-intercept form (y = mx + b), we simplify the equation to get:
y = -2/5x - 14/5