Question

identify the relationship between the graphs of these two equations.
$y = -\frac{5}{6}x + 5$
$y = -\frac{5}{6}x + 3$
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 \(y =-\frac{5}{6}x+3\), the slope \(m_2 =-\frac{5}{6}\).

Step2: Determine the relationship

Two lines are parallel if their slopes are equal (\(m_1=m_2\)) and they have different y - intercepts (to avoid being the same line). Here, \(m_1 = m_2=-\frac{5}{6}\) and the y - intercepts \(b_1 = 5\) and \(b_2=3\) are different. So the lines are parallel.

Answer:

parallel