Question

1. given j(x, -8) and k(-1, -5) and the graph of line l below, find the value of x so that (overline{jk}parallel l).

Explanation:

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

Pick two points on line \(l\), say \((0, 1)\) and \((- 2,-2)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So \(m_l=\frac{-2 - 1}{-2-0}=\frac{-3}{-2}=\frac{3}{2}\).

Step2: Find the slope of \(\overline{JK}\)

The slope of the line segment with endpoints \(J(x,-8)\) and \(K(-1,-5)\) is \(m_{JK}=\frac{-5-(-8)}{-1 - x}=\frac{-5 + 8}{-1 - x}=\frac{3}{-1 - x}\).

Step3: Set slopes equal

Since \(\overline{JK}\parallel l\), their slopes are equal. So \(\frac{3}{-1 - x}=\frac{3}{2}\).
Cross - multiply: \(3\times2=3\times(-1 - x)\).
\(6=-3 - 3x\).
Add \(3\) to both sides: \(6 + 3=-3x\), \(9=-3x\).
Divide both sides by \(-3\): \(x=-3\).

Answer:

\(x = - 3\)