Question

use the figure below to list the slopes m1, m2, m3, and m4 in order of decreasing size. choose the correct answer below. y = m3x + b3 y = m2x + b2 y = m1x + b1 y = m4x + b4

Explanation:

Step1: Recall slope - angle relationship

The slope \(m = \tan\theta\), where \(\theta\) is the angle the line makes with the positive \(x -\)axis. For lines with positive slopes, the larger the angle \(\theta\in(0,\frac{\pi}{2})\), the larger the slope. For lines with negative slopes, the larger the absolute - value of the angle \(\theta\in(\frac{\pi}{2},\pi)\), the smaller the slope.

Step2: Analyze the angles of the lines

Line \(y = m_3x + b_3\) has the largest positive angle with the positive \(x -\)axis among the four lines, so \(m_3\) is the largest positive slope. Line \(y = m_1x + b_1\) has a positive slope but a smaller angle than \(y = m_3x + b_3\), so \(m_1>0\) and \(m_1

Answer:

\(m_3, m_1, m_2, m_4\)