Question

determine which of the lines, if any, are parallel. explain.

Explanation:

Step1: Calculate slope of line \(a\)

Use slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line \(a\) with points \((-4,0)\) and \((0,3)\), \(m_a=\frac{3 - 0}{0-(-4)}=\frac{3}{4}\)

Step2: Calculate slope of line \(b\)

For line \(b\) with points \((0,0)\) and \((3,2)\), \(m_b=\frac{2 - 0}{3 - 0}=\frac{2}{3}\)

Step3: Calculate slope of line \(c\)

For line \(c\) with points \((-2,-3)\) and \((3,0)\), \(m_c=\frac{0-(-3)}{3-(-2)}=\frac{3}{5}\)

Step4: Check parallel condition

Parallel lines have equal slopes. Since \(m_a=\frac{3}{4}\), \(m_b=\frac{2}{3}\), \(m_c=\frac{3}{5}\), no two slopes are equal.

Answer:

No lines are parallel; the slopes are \(\frac{3}{4}\), \(\frac{2}{3}\), and \(\frac{3}{5}\) (all different)