Question

statements reasons

1. r || s given
2. $m_{r}=\frac{d - b}{c - 0}=\frac{d - b}{c}$

$m_{b}=\frac{0 - a}{c - 0}=-\frac{a}{c}$?

1. distance from $(0,b)$ to $(0,a)$ equals the distance from $(c,d)$ to $(c,0)$ definition of parallel lines
2. $d - 0 = b - a$ application of the distance formula
3. $m_{r}=\frac{(b - a)-b}{c}$ substitution property of equality
4. $m_{r}=\frac{a}{c}$ inverse property of addition
5. $m_{r}=m_{s}$ substitution property of equality

the table shows the proof of the relationship between the slopes of two parallel lines. what is the missing reason for step 2?
a. pythagorean theorem
b. application of the distance formula
c. transitive property
d. application of the slope formula

Explanation:

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line \(r\) with points \((0,b)\) and \((c,d)\), substituting into the slope formula gives \(m_r=\frac{d - b}{c-0}\). For line \(s\) with points \((0,a)\) and \((c,0)\), substituting into the slope formula gives \(m_s=\frac{0 - a}{c-0}\). So the reason for step 2 is the application of the slope formula.

Answer:

D. application of the slope formula