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 = m1x + b1 y = m3x + b3 y = m2x + b2 y = m4x + b4

Explanation:

Step1: Recall slope concept

The slope of a line $y = mx + b$ is a measure of its steepness. Positive - sloped lines go up from left to right and negative - sloped lines go down from left to right. Larger positive slopes mean steeper upward - sloping lines and larger negative slopes (in magnitude) mean steeper downward - sloping lines.

Step2: Analyze the lines in the figure

Lines with equations $y=m_1x + b_1$ and $y=m_3x + b_3$ have positive slopes since they are upward - sloping. The line $y = m_1x + b_1$ is steeper than the line $y=m_3x + b_3$, so $m_1>m_3>0$. Lines with equations $y=m_2x + b_2$ and $y=m_4x + b_4$ have negative slopes since they are downward - sloping. The line $y = m_4x + b_4$ is steeper (in the negative direction) than the line $y=m_2x + b_2$, so $m_2>m_4$ (where $m_2<0$ and $m_4<0$).

Step3: Order the slopes

Combining the above analysis, the order of the slopes in decreasing size is $m_1,m_3,m_2,m_4$.

Answer:

$m_1, m_3, m_2, m_4$