critical thinking questions: 25) fill in the blank so that the lines are not parallel: line a goes through…

Explanation:

Step1: Calculate slope of Line A

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For Line A with points $(0,8)$ and $(-2,0)$, we have $m_A=\frac{8 - 0}{0-(-2)}=\frac{8}{2} = 4$.

Step2: Set up slope - condition for non - parallel lines

Two lines are parallel if they have the same slope. Let the missing $y$ - value of Line B be $y$. The slope of Line B with points $(1,2)$ and $(3,y)$ is $m_B=\frac{y - 2}{3 - 1}=\frac{y - 2}{2}$. For the lines not to be parallel, $m_B\neq4$.

Step3: Solve for non - parallel condition

We set $\frac{y - 2}{2}\neq4$. Cross - multiply: $y-2\neq8$. Then $y\neq10$. So we can choose any value for $y$ except 10. For example, if we choose $y = 9$.

Answer:

9 (any value except 10 would be correct)