To solve this problem, let's work through the logic step-by-step and identify the missing reason for step 2:
1. Statement 1: [tex]\( r \| s \)[/tex] - Given.
2. Statement 2:
- For line [tex]\( r \)[/tex]: [tex]\( m_{r} = \frac{d - b}{c - 0} = \frac{d - b}{c} \)[/tex]
- For line [tex]\( s \)[/tex]: [tex]\( m_{s} = \frac{0 - a}{c - 0} = -\frac{a}{c} \)[/tex]
The reason for these formulas is the application of the slope formula. The slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by [tex]\( \frac{y_2 - y_1}{x_2 - x_1} \)[/tex].
Therefore, the missing reason for step 2 is:
B. application of the slope formula
The correct answer corresponds to the number 2.
