Final answer:
The equation in slope-intercept form for the line passing through (2, -2) and perpendicular to y = 2/5x + 2 is y = -5/2x + 3.
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. The given line has the slope of 2/5, so the line perpendicular to it will have a slope of -5/2. Now, 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 (2, -2) for (x1, y1) and -5/2 for m, we get y - (-2) = -5/2(x - 2). Simplifying this equation gives us y + 2 = -5/2x + 5. Finally, rearranging the equation in slope-intercept form, we get y = -5/2x + 3.