Line a passes through points (3, 13) and (6, 5). Line b is perpendicular to a. What is the slope of line b?
To find the slope of line a, we can use the formula:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of two points on the line. Using the given points \((3, 13)\) and \((6, 5)\) for line a, we have:
\[m_a = \frac{{5 - 13}}{{6 - 3}} = \frac{{-8}}{3}\]
Since line b is perpendicular to line a, the slope of line b must be the negative reciprocal of the slope of line a. Thus, the slope of line b is:
\[m_b = -\frac{1}{m_a} = -\frac{1}{\frac{{-8}}{3}} = \frac{3}{8}\]
Therefore, the slope of line b is \(m_b = \frac{3}{8}\).