Subjects algebra

Line Best Fit C2F764

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1. **State the problem:** We need to find the equation of the trend line (line of best fit) passing through the two yellow points on the scatter plot. 2. **Identify the points:** The two yellow points are approximately at $ (2, 0) $ and $ (8, 6) $. 3. **Formula for slope:** The slope $m$ of a line passing through points $ (x_1, y_1) $ and $ (x_2, y_2) $ is given by $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ 4. **Calculate the slope:** $$ m = \frac{6 - 0}{8 - 2} = \frac{6}{6} = 1 $$ 5. **Use slope-intercept form:** The equation of a line is $$ y = mx + b $$ where $m$ is the slope and $b$ is the y-intercept. 6. **Find the y-intercept $b$:** Substitute one point, for example $ (2, 0) $, and $m=1$ into the equation: $$ 0 = 1 \times 2 + b $$ $$ 0 = 2 + b $$ $$ b = -2 $$ 7. **Write the final equation:** $$ y = 1x - 2 $$ or simply $$ y = x - 2 $$ **Answer:** The equation of the trend line is $ y = x - 2 $.