Subjects algebra

Line Of Fit 9F9B00

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1. **State the problem:** We need to find the equation of the line of fit in slope-intercept form $y=mx+b$ using the points $(2001, 17.60)$ and $(2002, 18.75)$. 2. **Formula for slope:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)=(2001,17.60)$ and $(x_2,y_2)=(2002,18.75)$. 3. **Calculate the slope:** $$m=\frac{18.75 - 17.60}{2002 - 2001}=\frac{1.15}{1}=1.15$$ 4. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Substitute $m=1.15$ and point $(2001,17.60)$: $$y - 17.60 = 1.15(x - 2001)$$ 5. **Simplify to slope-intercept form:** $$y = 1.15x - 1.15 \times 2001 + 17.60$$ Calculate $1.15 \times 2001$: $$1.15 \times 2001 = 2301.15$$ So, $$y = 1.15x - 2301.15 + 17.60 = 1.15x - 2283.55$$ 6. **Final equation:** $$\boxed{y = 1.15x - 2283.55}$$ This equation models the average price of a major-league baseball ticket from 1997 to 2006 based on the given points.