Question

If line b is perpendicular to y = -1/3x + 12, which of the following MUST be true about line b?

I. The slope will be 3.
II. The y-intercept will be 12.
III. The lines will form a 90° angle.

Answer 1

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.