Question

line relationships find the slope of each line. identify any parallel or perpendicular lines. 33.

Explanation:

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

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(P(-4,-7)\) and \(Q(4,3)\).

$$ m_{PQ}=\frac{3-(-7)}{4 - (-4)}=\frac{3 + 7}{4+4}=\frac{10}{8}=\frac{5}{4} $$

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

Let \(W(0,5)\) and \(V(4,1)\).

$$ m_{WV}=\frac{1 - 5}{4-0}=\frac{-4}{4}=-1 $$

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

Let \(B(-4,-1)\) and \(A(0,-5)\).

$$ m_{BA}=\frac{-5-(-1)}{0-(-4)}=\frac{-5 + 1}{4}=\frac{-4}{4}=-1 $$

Step4: Identify parallel and perpendicular lines

Since \(m_{WV}=m_{BA}=-1\), lines \(WV\) and \(BA\) are parallel.
Check for perpendicularity: \(m_{PQ}\times m_{WV}=\frac{5}{4}\times(-1)=-\frac{5}{4}
eq - 1\), \(m_{PQ}\times m_{BA}=\frac{5}{4}\times(-1)=-\frac{5}{4}
eq - 1\)

Answer:

Slope of \(PQ\) is \(\frac{5}{4}\), slope of \(WV\) is \(-1\), slope of \(BA\) is \(-1\). Lines \(WV\) and \(BA\) are parallel.