Subjects algebra

Line Equation 744293

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1. **Problem Statement:** Given two points $(18600, 115000)$ and $(21320, 13000)$, find the equation of the line passing through these points. 2. **Formula Used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ The equation of the line in point-slope form is: $$y - y_1 = m(x - x_1)$$ 3. **Calculate the slope:** $$m = \frac{13000 - 115000}{21320 - 18600} = \frac{-102000}{2720} = -37.5$$ 4. **Write the equation using point $(18600, 115000)$:** $$y - 115000 = -37.5(x - 18600)$$ 5. **Simplify the equation:** $$y = -37.5x + 37.5 \times 18600 + 115000$$ Calculate $37.5 \times 18600$: $$37.5 \times 18600 = 697500$$ So, $$y = -37.5x + 697500 + 115000 = -37.5x + 812500$$ 6. **Final equation:** $$\boxed{y = -37.5x + 812500}$$ This is the linear function that passes through the given points.