Final answer:
The equation of the line that is perpendicular to y = -2x+3 and passes through the point (-4, -4) is y = ½x - 2, which is answer choice (c).
Step-by-step explanation:
The student is asking to determine the slope-intercept form of the equation of a line that passes through the point (-4, -4) and is perpendicular to the line with the equation y = -2x+3. To find the slope of a line perpendicular to another, we take the negative reciprocal of the original slope. Since the original line has a slope of -2, the slope of the perpendicular line is ½. We then use the point (-4, -4) to find the y-intercept, 'b', of the equation y = mx + b, where 'm' is the slope. Substituting the point into the equation, we get -4 = (½)(-4) + b, which simplifies to -4 = -2 + b; thus, b = -2. The final equation of the line is therefore y = ½x - 2, which corresponds to answer choice (c).