Question

1. line 1: (0, 1), (1, 3) line 2: (4, -1), (5, 2) slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ tell whether the lines through the given points are parallel, perpendicular or neither. a) perpendicular b) neither c) parallel

Explanation:

Step1: Calculate slope of Line 1

For Line 1 with points $(0,1)$ and $(1,3)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_1=\frac{3 - 1}{1 - 0}=\frac{2}{1}=2$.

Step2: Calculate slope of Line 2

For Line 2 with points $(4,-1)$ and $(5,2)$, using the slope formula, we get $m_2=\frac{2-(-1)}{5 - 4}=\frac{2 + 1}{1}=3$.

Step3: Analyze the relationship

Parallel lines have equal slopes ($m_1=m_2$), and perpendicular lines have slopes such that $m_1\times m_2=-1$. Here, $m_1 = 2$ and $m_2=3$, $m_1
eq m_2$ and $m_1\times m_2=2\times3 = 6
eq - 1$.

Answer:

B. Neither