Question

determine whether the pair of lines are parallel, perpendicular, or neither.\\(5x = 4y + 3\\)\\(-25x + 20y = 3\\)\\(\\)\\(\\)choose the correct answer below.\\(\bigcirc\\) a. perpendicular\\(\bigcirc\\) b. neither\\(\bigcirc\\) c. parallel

Explanation:

Step1: Rewrite first line to slope-intercept

Rearrange $5x=4y+3$ to $y=mx+b$:
$4y=5x-3$
$y=\frac{5}{4}x-\frac{3}{4}$
Slope $m_1=\frac{5}{4}$

Step2: Rewrite second line to slope-intercept

Rearrange $-25x+20y=3$ to $y=mx+b$:
$20y=25x+3$
$y=\frac{25}{20}x+\frac{3}{20}$
Simplify: $y=\frac{5}{4}x+\frac{3}{20}$
Slope $m_2=\frac{5}{4}$

Step3: Compare slopes

Parallel lines have equal slopes.
$m_1 = m_2 = \frac{5}{4}$

Answer:

C. Parallel