Question

four sets of data have the trend lines shown below.
data set 1\tdata set 2\tdata set 3\tdata set 4
y = 7.5x + 3.8\ty = 9.8x + 6.7\ty = 3.8x + 7.5\ty = 6.7x + 9.8
which trend line describes the set with the greatest rate of change?
○ y = 7.5x + 3.8
○ y = 9.8x + 6.7
○ y = 3.8x + 7.5
○ y = 6.7x + 9.8

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y-intercept.

Step2: Identify slopes of each line

• For \( y = 7.5x + 3.8 \), slope \( m_1 = 7.5 \)
• For \( y = 9.8x + 6.7 \), slope \( m_2 = 9.8 \)
• For \( y = 3.8x + 7.5 \), slope \( m_3 = 3.8 \)
• For \( y = 6.7x + 9.8 \), slope \( m_4 = 6.7 \)

Step3: Compare the slopes

Compare \( 7.5 \), \( 9.8 \), \( 3.8 \), and \( 6.7 \). We find that \( 9.8 \) is the largest.

Answer:

B. \( y = 9.8x + 6.7 \)