Question

determine if lines r and s are parallel.
select the correct choice below and fill in the answer box(es) to complete your choice.
a. the slope of line r is \\(\square\\), and the slope of line s is \\(\square\\). since the product of their slopes is -1, lines r and s are parallel.
(simplify your answers.)
b. since both lines have a slope of \\(\square\\), lines r and s are parallel.
(simplify your answer.)
c. the slope of line r is \\(\square\\), and the slope of line s is \\(\square\\). since the slopes are different, lines r and s are not parallel.
(simplify your answers.)
d. the slope of line r is \\(\square\\), and the slope of line s is \\(\square\\). since the product of their slopes is not -1, lines r and s are not parallel.
(simplify your answers.)

Explanation:

Step1: Identify points for line r

Choose two points on line r: e.g., $(0, 2)$ and $(4, 0)$

Step2: Calculate slope of line r

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$\text{Slope of } r = \frac{0 - 2}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}$

Step3: Identify points for line s

Choose two points on line s: e.g., $(0, -8)$ and $(4, -4)$

Step4: Calculate slope of line s

$\text{Slope of } s = \frac{-4 - (-8)}{4 - 0} = \frac{4}{4} = 1$

Step5: Compare slopes for parallelism

Parallel lines have equal slopes. $-\frac{1}{2}
eq 1$, so lines are not parallel.

Answer:

C. The slope of line r is $-\frac{1}{2}$, and the slope of line s is $1$. Since the slopes are different, lines r and s are not parallel.