Question

critical thinking questions: 25) fill in the blank so that the lines are not parallel: line a goes through (0, 8) and (-2, 0) line b goes through (1, 2) and (3, _)

Explanation:

Step1: Find 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: Let the slope of Line B be $m_B$

For two non - parallel lines, their slopes are not equal. For Line B with points $(1,2)$ and $(3,y)$, the slope $m_B=\frac{y - 2}{3 - 1}=\frac{y - 2}{2}$.

Step3: Set $m_B

eq m_A$
We want $\frac{y - 2}{2}
eq4$. Cross - multiply to get $y-2
eq8$. Then $y
eq10$. So we can choose any value for $y$ except $10$, for example $y = 9$.

Answer:

9 (any value except 10 would be correct)