Question

4
equation of the trend line:
5
equation of the trend line:
6
equation of the trend line:
7 y
8 v
9

Explanation:

Step1: Analyze Graph 4

• Identify two points on the trend line. Let's take (0, 8) and (10, 4).
• Calculate the slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 8}{10 - 0} = \frac{-4}{10} = -0.4 \).
• The y-intercept \( b \) is 8 (when \( x = 0 \)).
• Equation: \( y = -0.4x + 8 \) or \( y = -\frac{2}{5}x + 8 \).

Step2: Analyze Graph 5

• Points on trend line: (0, 8) and (40, 0).
• Slope \( m = \frac{0 - 8}{40 - 0} = \frac{-8}{40} = -0.2 \).
• Y-intercept \( b = 8 \).
• Equation: \( y = -0.2x + 8 \) or \( y = -\frac{1}{5}x + 8 \).

Step3: Analyze Graph 6

• Points on trend line: (0, 70) and (10, 10) (approximate, or (0, 70) and (10, 10) for clear slope). Wait, better: (0, 70) and (10, 10)? No, let's take (0, 70) and (10, 10)? Wait, looking at the graph, when \( x = 0 \), \( y \approx 70 \), and when \( x = 10 \), \( y \approx 10 \). Wait, no, the line goes from (0,70) to (10,10)? Wait, no, let's check the grid. The y-axis at x=0 is 70? Wait, the graph 6: y-axis has 80, 60, 40, 20. So when x=0, y is 70 (between 60 and 80), and when x=10, y is 10? Wait, no, the line is from (0,70) to (10,10)? Wait, slope \( m = \frac{10 - 70}{10 - 0} = \frac{-60}{10} = -6 \). Wait, no, maybe (0,70) and (10,10) is wrong. Wait, let's take two points: (0,70) and (5,40). Then slope \( m = \frac{40 - 70}{5 - 0} = \frac{-30}{5} = -6 \). Then y-intercept is 70. So equation \( y = -6x + 70 \). Wait, but let's check again. Alternatively, (0,70) and (10,10): slope -6, y-intercept 70. So equation \( y = -6x + 70 \).

Answer:

Graph 4: \( y = -0.4x + 8 \) (or \( y = -\frac{2}{5}x + 8 \))
Graph 5: \( y = -0.2x + 8 \) (or \( y = -\frac{1}{5}x + 8 \))
Graph 6: \( y = -6x + 70 \) (approximate, based on the trend line)