Question

line u passes through points (10, 9) and (7, 5). line v is perpendicular to u. what is the slope of line v? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Find slope of line u

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For points \((10,9)\) and \((7,5)\), \(x_1 = 10\), \(y_1 = 9\), \(x_2 = 7\), \(y_2 = 5\). So slope of \(u\) is \(\frac{5 - 9}{7 - 10}=\frac{-4}{-3}=\frac{4}{3}\).

Step2: Find slope of line v

If two lines are perpendicular, the product of their slopes is \(- 1\). Let slope of \(v\) be \(m_v\). Then \(\frac{4}{3}\times m_v=-1\), so \(m_v =-\frac{3}{4}\).

Answer:

\(-\frac{3}{4}\)