Subjects algebra

Line Slope 6Eacf4

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1. **State the problem:** We need to find the slope of the line that relates the area of a garden (in ft²) to the cost to cover it with landscaping stones. 2. **Recall the formula for slope:** The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Identify the points from the graph:** The line passes through $(0, 0)$ and $(45, 180)$. 4. **Calculate the slope:** $$m = \frac{180 - 0}{45 - 0} = \frac{180}{45}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{180}}{\cancel{45}} = 4$$ 6. **Interpretation:** The slope of 4 means that for every 1 ft² increase in area, the cost increases by 4 units. **Final answer:** The slope of the line is $4$.