To determine the slope of the line in the graph representing the transporting cost versus the weight of sugar, we need to analyze two points on the line. Since I don't have access to the graph, I will explain how you can find the slope.
(a) Finding the Slope
The slope (\(m\)) of a line is calculated using the formula:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Where:
- \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.
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Select Two Points: Choose two points from the graph. For example, if one point is (1, 125) and another point is (9, 1000):
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Calculate the Slope: Using the coordinates of these points:
- \(x_1 = 1\), \(y_1 = 125\)
- \(x_2 = 9\), \(y_2 = 1000\)
Plug these values into the slope formula: \[ m = \frac{1000 - 125}{9 - 1} = \frac{875}{8} = 109.375 \]
So, the slope of the line is \(109.375\).
(b) Cost Increase per Ton
The cost increase per ton of sugar being transported is equal to the slope of the line. Therefore, in this case:
- The cost increases by $109.375 for each ton of sugar being transported.
You can apply the same process using the specific points from the graph you have. If you find different points or slope values, just replace the numbers in the calculations accordingly.
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