Final answer:
The slope-intercept form of the equation of the line described is y = -2x - 5.
Step-by-step explanation:
The given line has a slope of 1/2. Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the line perpendicular to y = 1/2x - 4 is -2/1 or -2.
Using the point-slope form of a linear equation, we can write the equation of the perpendicular line as y - y1 = m(x - x1), where (x1, y1) is the given point (-4, 3) and m is the slope (-2).
Substituting the values, we have y - 3 = -2(x - (-4)). Simplifying, we get y - 3 = -2(x + 4). Finally, rearranging the equation into slope-intercept form, we have y = -2x - 5.