Subjects algebra

Line Equation D5Eff5

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1. **State the problem:** We need to find the equation of the straight line in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 2. **Identify points on the line:** From the description, the line passes near $(0,6)$ and crosses the x-axis between $1$ and $2$. It also passes through approximately $(2,-4)$. 3. **Find the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(0,6)$ and $(2,-4)$: $$m = \frac{-4 - 6}{2 - 0} = \frac{-10}{2} = -5$$ 4. **Find the y-intercept $c$:** Since the line passes through $(0,6)$, the y-intercept is $c = 6$. 5. **Write the equation:** Substitute $m$ and $c$ into $y = mx + c$: $$y = -5x + 6$$ **Final answer:** $y = -5x + 6$