Question

use the figure below to list the slopes ( m_1 ), ( m_2 ), ( m_3 ), and ( m_4 ) in order of decreasing size.
choose the correct answer below.
( m_3, m_2, m_1, m_4 )
( m_4, m_1, m_2, m_3 )
( m_1, m_4, m_3, m_2 )
( m_4, m_2, m_1, m_3 )

Explanation:

Step1: Recall Slope Properties

The slope of a line \( y = mx + b \) determines its steepness and direction. Positive slopes go up from left to right, negative slopes go down. Steeper lines (closer to vertical) have larger absolute values. For positive slopes, steeper means larger \( m \); for negative slopes, steeper (more negative) means smaller \( m \) (more negative is less than less negative).

Step2: Analyze Each Line

• \( y = m_4x + b_4 \) and \( y = m_1x + b_1 \): Positive slopes (upward). \( m_4 \) is steeper than \( m_1 \), so \( m_4 > m_1 \).
• \( y = m_2x + b_2 \): Positive, very gentle (close to horizontal), so \( m_2 \) is small positive, \( m_1 > m_2 \), \( m_4 > m_2 \).
• \( y = m_3x + b_3 \): Negative slope (downward), so \( m_3 < 0 \), and it's the only negative slope here, so it's the smallest.

Step3: Order by Decreasing Size

From largest to smallest: \( m_4 \) (steep positive), \( m_1 \) (less steep positive), \( m_2 \) (gentle positive), \( m_3 \) (negative). So order is \( m_4, m_1, m_2, m_3 \).

Answer:

B. \( m_4, m_1, m_2, m_3 \)