Question

line e passes through points (10,8) and (1,1). line f passes through points (1,3) and (10,10). are line e and line f parallel or perpendicular?

Explanation:

Step1: Calculate the slope of line e

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line e with points \((x_1 = 1,y_1 = 1)\) and \((x_2 = 10,y_2 = 8)\), \(m_e=\frac{8 - 1}{10 - 1}=\frac{7}{9}\)

Step2: Calculate the slope of line f

For line f with points \((x_1 = 1,y_1 = 3)\) and \((x_2 = 10,y_2 = 10)\), \(m_f=\frac{10 - 3}{10 - 1}=\frac{7}{9}\)

Step3: Determine the relationship

Since \(m_e=m_f=\frac{7}{9}\), by the definition of parallel lines (two lines with the same slope are parallel), line e and line f are parallel.

Answer:

parallel