Question

determine if the lines defined by the given equations are parallel, perpendicular, or neither.

\\8x = 5y\\
\\\frac{5}{4}x - 2y = 0\\

the lines are

• parallel
• perpendicular
• neither parallel nor perpendicular

Explanation:

Step1: Find the slope of the first line

$$8x = 5y \implies y = \frac{8}{5}x \implies m_1 = \frac{8}{5}$$

Step2: Find the slope of the second line

$$\frac{5}{4}x - 2y = 0 \implies 2y = \frac{5}{4}x \implies y = \frac{5}{8}x \implies m_2 = \frac{5}{8}$$

Step3: Compare the slopes of both lines

$$m_1 eq m_2 \text{ and } m_1 \cdot m_2 = 1 eq -1$$

Answer:

neither parallel nor perpendicular