Question

4, given ( j(-8,-18), k(2,7), l(-1,9) ), and ( m(x,4) ), find the value of ( x ) so that ( overline{jk} parallel overline{lm} ). ( \frac{7-(-18)}{2-(-8)}=\frac{4-9}{x-(-1)} )

Explanation:

Step1: Calculate the slope of \(\overline{JK}\)

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For points \(J(-8,-18)\) and \(K(2,7)\), we have \(y_2 = 7\), \(y_1=-18\), \(x_2 = 2\), \(x_1=-8\).

$$m_{JK}=\frac{7-(-18)}{2-(-8)}=\frac{7 + 18}{2 + 8}=\frac{25}{10}=\frac{5}{2}$$

Step2: Calculate the slope of \(\overline{LM}\)

For points \(L(-1,9)\) and \(M(x,4)\), using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \(y_2 = 4\), \(y_1 = 9\), \(x_2=x\), \(x_1=-1\)

$$m_{LM}=\frac{4 - 9}{x-(-1)}=\frac{-5}{x + 1}$$

Step3: Set the slopes equal (since \(\overline{JK}\parallel\overline{LM}\), their slopes are equal)

Since \(m_{JK}=m_{LM}\), we have \(\frac{5}{2}=\frac{-5}{x + 1}\)
Cross - multiply: \(5(x + 1)=-5\times2\)

$$5x+5=-10$$

Subtract 5 from both sides: \(5x=-10 - 5\)

$$5x=-15$$

Divide both sides by 5: \(x=\frac{-15}{5}=-3\)

Answer:

\(x=-3\)