To determine the slope of a line that is perpendicular to another line, we need to understand a fundamental concept from geometry regarding slopes. The key principle is that the slopes of two perpendicular lines are negative reciprocals of each other.
In mathematical terms, if you have a line with a slope m, the slope of a line perpendicular to it is given by:
m_perpendicular = -1 / mIn this specific case, the slope of the given line is m = 13. To find the slope of a line perpendicular to this line, you substitute m into the formula:
m_perpendicular = -1 / 13Thus, the slope of the line that is perpendicular to the line with a slope of 13 is:
m_perpendicular = -1/13This result tells us that if you were to graph both lines, they would intersect at a right angle (90 degrees), and the steepness of the perpendicular line would be much less compared to the original line due to its negative value.