Line q passes through points (2, 17) and (4, 8). Line r is perpendicular to q. What is the slope of line r?

To find the slope of line r, we first need to find the slope of line q. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1).

Step 1: Find the slope of line q The slope of line q (m_q) passing through points (2, 17) and (4, 8) is: m_q = (8 - 17) / (4 - 2) = -9 / 2 = -4.5

Step 2: Find the slope of line r The slope of a line r that is perpendicular to another line with slope m is given by the negative reciprocal of m. The negative reciprocal of a number is found by flipping the number's fraction and changing its sign.

So, the slope of line r (m_r) is the negative reciprocal of m_q: m_r = -1 / m_q = -1 / -4.5 = 1 / 4.5 = 0.2222

So, the slope of line r is approximately 0.2222.