Question

determine which of the lines, if any, are parallel or perpendicular. explain.
14
______ are parallel. the slopes are
______
____ perpendicular to __. the slopes are ____

Explanation:

Step1: Calculate slope of line \(a\)

Use slope formula \(m=\frac{y_2-y_1}{x_2-x_1}\) with points \((-1,1)\) and \((2,0)\):
\(m_a=\frac{0-1}{2-(-1)}=\frac{-1}{3}=-\frac{1}{3}\)

Step2: Calculate slope of line \(b\)

Use slope formula with points \((0,5)\) and \((3,4)\):
\(m_b=\frac{4-5}{3-0}=\frac{-1}{3}=-\frac{1}{3}\)

Step3: Calculate slope of line \(c\)

Use slope formula with points \((0,0)\) and \((2,5)\):
\(m_c=\frac{5-0}{2-0}=\frac{5}{2}\)? No, correction: use \((0,0)\) and \((1,3)\) (from grid, line \(c\) rises 3 over 1):
\(m_c=\frac{3-0}{1-0}=3\)

Step4: Identify parallel lines

Lines with equal slopes are parallel: \(m_a=m_b=-\frac{1}{3}\), so \(a \parallel b\)

Step5: Identify perpendicular lines

Check product of slopes: \(m_a \times m_c = -\frac{1}{3} \times 3 = -1\), so \(c \perp a\) (and \(c \perp b\))

Answer:

Line \(a\) and Line \(b\) are parallel. The slopes are \(-\frac{1}{3}\)
Line \(c\) is perpendicular to Line \(a\) (and Line \(b\)). The slopes are \(3\) and \(-\frac{1}{3}\)