Final answer:
The correct equation of a line perpendicular to y = -2/3x and passing through (-6, -5) is y = 3/2x + 4, identified as option b.
Step-by-step explanation:
The question asks which of the following equations describes a line that is perpendicular to the line described by y = -2/3x and passes through the point (-6, -5). To find the equation of a line perpendicular to another, we need to determine the negative reciprocal of the original line's slope. Since the slope of the given line is -2/3, the slope of the line perpendicular to it would be 3/2. Thus, we are looking for an equation with a slope of 3/2.
We'll use the point-slope form of the equation of a line which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in our values, we get y + 5 = (3/2)(x + 6). Simplifying, we get y = (3/2)x + 4 when we move -5 to the right side and distribute the slope across x + 6.
The correct equation that describes the line is thus y = 3/2x + 4, which corresponds to option b.