Question

question given s(0, - 5), t(-6,0), u(-3,1), and v(-9,y). find y such that st || uv.

Explanation:

Step1: Find the slope of $\overline{ST}$

The slope formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $S(0,-5)$ and $T(-6,0)$, we have $x_1 = 0,y_1=-5,x_2=-6,y_2 = 0$. Then $m_{ST}=\frac{0-(-5)}{-6 - 0}=\frac{5}{-6}=-\frac{5}{6}$.

Step2: Find the slope of $\overline{UV}$

For points $U(-3,1)$ and $V(-9,y)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_{UV}=\frac{y - 1}{-9-(-3)}=\frac{y - 1}{-6}$.

Step3: Set the slopes equal

Since $\overline{ST}\parallel\overline{UV}$, their slopes are equal. So $-\frac{5}{6}=\frac{y - 1}{-6}$.
Cross - multiply: $(-5)\times(-6)=6\times(y - 1)$.
$30 = 6y-6$.
Add 6 to both sides: $30 + 6=6y$, so $36 = 6y$.
Divide both sides by 6: $y = 6$.

Answer:

$6$