Question

Line b passes through points (4, 13) and (7, 8). Line c is perpendicular to b. What is the slope of line c?

a) -1
b) 1
c) 1/3
d) -3

Answer 1

The slope of line c, perpendicular to line b, is 1/3, determined by taking the negative reciprocal of the slope of line b (which is -5/3).Thus the correct option is:c) 1/3

Step-by-step explanation:

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. Given that the slope of line b can be calculated as (change in y) / (change in x) between the two points (4, 13) and (7, 8), which is (8 - 13) / (7 - 4) = -5 / 3. The negative reciprocal of -5/3 is 3/5. Therefore, the slope of line c is 3/5, and the correct answer is c) 1/3.

To further explain, when two lines are perpendicular, the product of their slopes is -1. In this case, the slope of line b is -5/3, and the slope of line c is the negative reciprocal of -5/3, which is 3/5. This ensures that the product of the slopes is (-5/3) * (3/5) = -1, confirming the perpendicular relationship between the two lines. Thus, option c) 1/3 is the correct answer for the slope of line c.Thus the correct option is:c) 1/3