Subjects algebra

Line Equation F61045

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Question: What is the equation of the line shown below? Give your answer in the form $y = mx + c$ Graph: A straight decreasing line crosses the y-axis at $(0, 25)$ and the x-axis at $(8.33, 0)$, approximately.
1. **State the problem:** Find the equation of the line in the form $y = mx + c$ given it crosses the y-axis at $(0, 25)$ and the x-axis at approximately $(8.33, 0)$. 2. **Recall the formula:** The equation of a line is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 3. **Identify the y-intercept:** From the point $(0, 25)$, we see that $c = 25$. 4. **Calculate the slope $m$:** The slope is given by $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 25}{8.33 - 0} = \frac{-25}{8.33}.$$ 5. **Simplify the slope:** $$m = -\frac{25}{8.33} \approx -3.0.$$ 6. **Write the equation:** Substitute $m$ and $c$ into $y = mx + c$: $$y = -3.0x + 25.$$ 7. **Final answer:** The equation of the line is $$\boxed{y = -3x + 25}.$$