Final answer:
The slope of line b must be 3 and the lines must form a 90° angle, but the y-intercept of line b is not determined and can be any value.
Step-by-step explanation:
If line b is perpendicular to y = -1/3x + 12, then certain characteristics about line b must be true. The concept of slope in algebra states that perpendicular lines have opposite reciprocal slopes. That is, if one line has a slope m, the line perpendicular to it will have a slope of -1/m. Given that the slope of the original line is -1/3, the slope of the perpendicular line b would therefore be 3.
Statement I is true: The slope of line b will be 3.
Statement II is not necessarily true: The y-intercept of line b could be any value. Just because the original line has a y-intercept of 12 does not determine the y-intercept of line b; it could intersect the y-axis anywhere.
Statement III is true: The lines will form a 90° angle because per definition, perpendicular lines intersect at 90 degrees.