Question

the equation of line s is y = (8/7)x + 5/4. the equation of line t is y = (8/7)x + 1/6. are line s and line t parallel or perpendicular? parallel perpendicular neither submit

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Step2: Identify slopes of line s and line t

For line \( s \): \( y=\frac{8}{7}x+\frac{5}{4} \), so the slope \( m_s=\frac{8}{7} \).
For line \( t \): \( y=\frac{8}{7}x+\frac{1}{6} \), so the slope \( m_t=\frac{8}{7} \).

Step3: Determine parallel or perpendicular

Two lines are parallel if their slopes are equal (\( m_1 = m_2 \)) and perpendicular if the product of their slopes is \( - 1 \) (\( m_1\times m_2=-1 \)).
Here, \( m_s = m_t=\frac{8}{7} \), so they are parallel.

Answer:

parallel