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 slope of line \( l \)

Identify two points on line \( l \). From the graph, let's take the lower point \((-2, -4)\) and the upper point \((0, 2)\) (or other clear points). The slope \( m \) is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \((-2, -4)\) and \((0, 2)\): \( m=\frac{2 - (-4)}{0 - (-2)}=\frac{6}{2}=3 \).

Step2: Set slope of \( \overline{JK} \) equal to slope of \( l \)

Points \( J(x, -8) \) and \( K(-1, -5) \). The slope of \( \overline{JK} \) is \( \frac{-5 - (-8)}{-1 - x}=\frac{3}{-1 - x} \). Since \( \overline{JK} \parallel l \), their slopes are equal: \( \frac{3}{-1 - x}=3 \).

Step3: Solve for \( x \)

Multiply both sides by \((-1 - x)\): \( 3 = 3(-1 - x) \). Divide both sides by 3: \( 1=-1 - x \). Add 1 to both sides: \( 2=-x \), so \( x = -2 \).

Answer:

\( x = -2 \)