Question

name addison v. date 12-17-25
scatter plots: line of best fit
write the slope-intercept form equation of the trend line of each scatter plot.
1.
scatter plot with x from 0 to 10, y from 0 to 10, trend line drawn
equation of the trend line:
y=
2.
scatter plot with x from 0 to 10, y from 0 to 30, trend line drawn
equation of the trend line:
3.
scatter plot with x from 0 to 25, y from 0 to 90, trend line drawn
equation of the trend line:
y=
4.
scatter plot with x from 0 to 10, y from 0 to 20, trend line drawn
equation of the trend line:
5.
scatter plot with x from 0 to 50, y from 0 to 10, trend line drawn
equation of the trend line:
y=
6.
scatter plot with x from 0 to 10, y from 0 to 80, trend line drawn
equation of the trend line:
7.
scatter plot with x from 0 to 5, y from 0 to 48, trend line drawn
equation of the trend line:
y=
8.
scatter plot with x from 0 to 10, y from 0 to 40, trend line drawn
equation of the trend line:
9.
scatter plot with x from 0 to 100, y from 0 to 50, trend line drawn
equation of the trend line:
y=

Explanation:

Step1: Analyze Graph 1 (Top-Left)

• Identify Points: The trend line passes through \((0, 9)\) (y-intercept, \(b = 9\)) and another point, e.g., \((9, 6)\).
• Calculate Slope: \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 - 9}{9 - 0}=\frac{-3}{9}=-\frac{1}{3}\).
• Slope-Intercept Form: \(y = mx + b\), so \(y = -\frac{1}{3}x + 9\).

Step2: Analyze Graph 2 (Top-Middle)

• Identify Points: Trend line passes through \((0, 10)\) (\(b = 10\)) and \((9, 20)\).
• Calculate Slope: \(m=\frac{20 - 10}{9 - 0}=\frac{10}{9}\approx1.11\) (or use \((3, 14)\): \(m=\frac{14 - 10}{3 - 0}=\frac{4}{3}\)). Wait, recheck: From \((0,10)\) to \((6,18)\): \(m=\frac{18 - 10}{6 - 0}=\frac{8}{6}=\frac{4}{3}\). So \(y=\frac{4}{3}x + 10\).

Step3: Analyze Graph 3 (Top-Right)

• Identify Points: Trend line passes through \((0, 5)\) (approx) and \((25, 30)\).
• Calculate Slope: \(m=\frac{30 - 5}{25 - 0}=\frac{25}{25}=1\). Wait, \((0,5)\) to \((25,30)\): \(m=\frac{30 - 5}{25 - 0}=1\), so \(y = x + 5\) (or check \((5,10)\): \(10 = 5 + 5\), correct).

Step4: Analyze Graph 4 (Middle-Left)

• Identify Points: Trend line passes through \((0, 9)\) (\(b = 9\)) and \((10, 4)\).
• Calculate Slope: \(m=\frac{4 - 9}{10 - 0}=\frac{-5}{10}=-\frac{1}{2}\). So \(y = -\frac{1}{2}x + 9\).

Step5: Analyze Graph 5 (Middle-Middle)

• Identify Points: Trend line passes through \((0, 8)\) (\(b = 8\)) and \((40, 0)\).
• Calculate Slope: \(m=\frac{0 - 8}{40 - 0}=\frac{-8}{40}=-\frac{1}{5}\). Wait, recheck: From \((0,8)\) to \((20,4)\): \(m=\frac{4 - 8}{20 - 0}=\frac{-4}{20}=-\frac{1}{5}\)? No, \((0,8)\) to \((40,0)\): \(m=\frac{0 - 8}{40 - 0}=-\frac{1}{5}\)? Wait, \(8\) to \(0\) over \(40\) is \(-\frac{1}{5}\), so \(y = -\frac{1}{5}x + 8\).

Step6: Analyze Graph 6 (Middle-Right)

• Identify Points: Trend line passes through \((0, 70)\) (approx) and \((10, 10)\). Wait, no: \((0,70)\) to \((10,10)\): \(m=\frac{10 - 70}{10 - 0}=\frac{-60}{10}=-6\)? No, recheck: The line goes from \((0,70)\) to \((10,10)\)? No, the graph has \(x\) up to 10, \(y\) down to 10. Wait, \((0,70)\) and \((10,10)\): \(m=-6\), but maybe \((0,70)\) and \((9,15)\): \(m=\frac{15 - 70}{9 - 0}=\frac{-55}{9}\approx -6.11\). Alternatively, \((0,70)\) and \((10,10)\): \(y = -6x + 70\).

Step7: Analyze Graph 7 (Bottom-Left)

• Identify Points: Trend line passes through \((0, 0)\) (\(b = 0\)) and \((5, 15)\).
• Calculate Slope: \(m=\frac{15 - 0}{5 - 0}=3\). So \(y = 3x\).

Step8: Analyze Graph 8 (Bottom-Middle)

• Identify Points: Trend line passes through \((0, 30)\) (\(b = 30\)) and \((9, 25)\).
• Calculate Slope: \(m=\frac{25 - 30}{9 - 0}=\frac{-5}{9}\approx -0.56\). Wait, \((0,30)\) to \((9,25)\): \(m=-\frac{5}{9}\), so \(y = -\frac{5}{9}x + 30\).

Step9: Analyze Graph 9 (Bottom-Right)

• Identify Points: Trend line passes through \((0, 30)\) (\(b = 30\)) and \((30, 50)\).
• Calculate Slope: \(m=\frac{50 - 30}{30 - 0}=\frac{20}{30}=\frac{2}{3}\). So \(y=\frac{2}{3}x + 30\).

Answer:

1. \( y = -\frac{1}{3}x + 9 \)
2. \( y = \frac{4}{3}x + 10 \)
3. \( y = x + 5 \) (or \( y = x + 5 \) based on points)
4. \( y = -\frac{1}{2}x + 9 \)
5. \( y = -\frac{1}{5}x + 8 \) (or adjusted)
6. \( y = -7x + 70 \) (corrected: recheck \((0,70)\) to \((10,0)\): \(m=-7\), so \(y = -7x + 70\))
7. \( y = 3x \)
8. \( y = -\frac{1}{2}x + 30 \) (recheck: \((0,30)\) to \((10,25)\): \(m=-0.5\), so \(y = -0.5x + 30\) or \(y = -\frac{1}{2}x + 30\))
9. \( y = \frac{2}{3}x + 30 \)

(Note: Some slopes may need minor adjustments based on exact trend line points, but the process follows identifying \(b\) (y-intercept) and calculating \(m\) from two points on the trend line.)