Question

question given l(6, - 5), m(3, - 6), n(8, 4), and o(x, - 2). find x such that lm || no.

Explanation:

Step1: Find slope of line LM

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $L(6,-5)$ and $M(3,-6)$, we have $m_{LM}=\frac{-6-(-5)}{3 - 6}=\frac{-6 + 5}{-3}=\frac{-1}{-3}=\frac{1}{3}$.

Step2: Find slope of line NO

For points $N(8,4)$ and $O(x,-2)$, the slope $m_{NO}=\frac{-2 - 4}{x - 8}=\frac{-6}{x - 8}$.

Step3: Set slopes equal

Since $LM\parallel NO$, their slopes are equal. So $\frac{1}{3}=\frac{-6}{x - 8}$.

Step4: Cross - multiply

Cross - multiplying gives $x−8=-18$.

Step5: Solve for x

Adding 8 to both sides, we get $x=-18 + 8=-10$.

Answer:

$x=-10$