Question

identify the relationship between the graphs of these two equations.
$y = \frac{5}{6}x + 5$
$y = \frac{5}{6}x - 1$
click on the correct answer.
parallel
perpendicular
neither

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.
For the first equation \(y=\frac{5}{6}x + 5\), the slope \(m_1=\frac{5}{6}\).
For the second equation \(y=\frac{5}{6}x-1\), the slope \(m_2=\frac{5}{6}\).

Step2: Determine the relationship

• Parallel lines have equal slopes (\(m_1 = m_2\)) and different y - intercepts.
• Perpendicular lines have slopes that are negative reciprocals (\(m_1\times m_2=- 1\)).
• If neither of these conditions is met, the lines are neither parallel nor perpendicular.

Here, \(m_1 = m_2=\frac{5}{6}\) and the y - intercepts (\(5\) and \(- 1\)) are different. So the lines are parallel.

Answer:

parallel