6 answers
To find the slope of the line passing through points \( A(5, 6) \) and \( B(15, 12) \), you can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = (5, 6) \) and \( (x_2, y_2) = (15, 12) \). Plugging in the values:
\[ m = \frac{12 - 6}{15 - 5} = \frac{6}{10} = \frac{3}{5} \]
Thus, the slope of the line \( n \) is \( \frac{3}{5} \).
To find the slope of the line passing through points \( A(15, -2) \) and \( B(-5, 2) \), you can use the formula for the slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = (15, -2) \) and \( (x_2, y_2) = (-5, 2) \). Plugging in the values:
\[ m = \frac{2 - (-2)}{-5 - 15} = \frac{2 + 2}{-5 - 15} = \frac{4}{-20} = -\frac{1}{5} \]
Thus, the slope of line \( M \) is \( -\frac{1}{5} \).
Steamboats and canals played a crucial role in facilitating westward travel and expansion in the United States during the 19th century for several reasons:
Improved Transportation Efficiency: Steamboats made travel and the transport of goods faster and more efficient compared to traditional methods such as flatboats or sailing ships. With the power of steam, these vessels could navigate rivers and lakes more reliably and at a greater speed.
Cost-Effective Freight Transport: The use of steamboats significantly reduced the cost of transporting goods. This was especially beneficial for agricultural and industrial products, allowing farmers and manufacturers in the West to access broader markets and thus improving their economic viability.
Facilitation of Trade and Settlement: Canals, such as the Erie Canal, connected different waterways, allowing for the movement of goods between distant regions. This interconnectedness facilitated trade, making it easier for settlers to obtain supplies and for producers to ship their products. The success of canals also encouraged settlement in the Midwest and beyond.
Accessibility and Connectivity: Steamboats and canals opened up remote areas that were previously difficult to access. By linking rivers and land routes, they provided reliable transportation links that made it feasible for more people to settle in the West and for goods to flow in and out of these regions.
Economic Opportunities: As transportation improved, so did economic opportunities for individuals and families. Those traveling westward could transport their belongings more easily, and new communities quickly emerged around canal and steamboat hubs, fostering economic growth.
Cultural Exchange and Migration: The increased mobility allowed not only for the transport of goods but also for people. It encouraged migration to western territories, enabling cultural exchange and the spread of ideas, technologies, and lifestyles.
In summary, steamboats and canals significantly enhanced the capacity for transportation and trade during the westward expansion of the United States, facilitating the movement of people and goods, which contributed to the economic development and settlement of the Western territories.
1 answer
1 answer
1 answer
3 answers