Question

line relationships find the slope of each line. identify any parallel or perpendicular lines. 35.

Explanation:

Step1: Find the slope of line \(A\)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's assume two points on line \(A\) (say \((- 3,-4)\) and \((0,-1)\)).

$$m_A=\frac{-1-(-4)}{0 - (-3)}=\frac{-1 + 4}{0+3}=\frac{3}{3}=1$$

Step2: Find the slope of line \(C\)

Let's assume two points on line \(C\) (say \((-3,2)\) and \((0,4)\)).

$$m_C=\frac{4 - 2}{0-(-3)}=\frac{2}{3}$$

Step3: Find the slope of line \(Z\)

Let's assume two points on line \(Z\) (say \((0,0)\) and \((3,3)\)).

$$m_Z=\frac{3-0}{3 - 0}=1$$

Step4: Check for parallel and perpendicular lines

Two lines are parallel if \(m_1=m_2\). Since \(m_A = 1\) and \(m_Z=1\), lines \(A\) and \(Z\) are parallel.
Two lines are perpendicular if \(m_1\times m_2=- 1\). Here, \(m_A\times m_C=1\times\frac{2}{3}=\frac{2}{3}
eq - 1\), \(m_C\times m_Z=\frac{2}{3}\times1=\frac{2}{3}
eq - 1\)

Answer:

Slope of line \(A\): \(1\); Slope of line \(C\): \(\frac{2}{3}\); Slope of line \(Z\): \(1\). Parallel lines: \(A\) and \(Z\)