Question

in exercises 3-5, tell whether the lines through the given points are parallel.

Explanation:

Step1: Recall slope - formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate slope of first line

Let's assume two points on the first line are \((x_1,y_1)\) and \((x_2,y_2)\). For example, if we take two points \((-1,4)\) and \((3,2)\) on one of the lines, then \(m_1=\frac{2 - 4}{3-(-1)}=\frac{-2}{4}=-\frac{1}{2}\).

Step3: Calculate slope of second line

Take two points on the second line, say \((-3,-2)\) and \((1,0)\). Then \(m_2=\frac{0 - (-2)}{1-(-3)}=\frac{2}{4}=\frac{1}{2}\).

Step4: Compare slopes

Parallel lines have equal slopes. Since \(m_1
eq m_2\), the lines are not parallel.

Answer:

The lines are not parallel.