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Understanding the concept of slope and intercept is crucial when dealing with linear equations like the one given for the weight of adult blue whales. Let's break it down:

• The **slope**, denoted as \( m \) in the equation, measures how steep a line is. It tells us how much the weight \( W \) changes for each unit increase in length \( L \). For the equation \( W = 3.51L - 192 \), the slope is 3.51. This means for each additional foot in length, the whale's weight increases by 3.51 British tons.
• The **intercept**, denoted as \( b \), is where the line crosses the vertical axis (W-axis). In our equation, the intercept is -192. This indicates that if we could theoretically have a blue whale with a zero length (which doesn't actually exist), its initial weight on our graph would start at -192 tons.

By using these two components, you can easily reconstruct and understand how the line represents the relationship between length and weight.

Graphing linear functions involves visually representing the equation on a coordinate system. Here’s how you can graph the function \( W = 3.51L - 192 \):- Start by plotting the **y-intercept** on the W-axis. In our equation, this point is -192.- Use the **slope** to determine how the line ascends. For every 1 unit increase in \( L \), the weight \( W \) increases by 3.51. So, after marking the intercept, move up 3.51 units vertically and 1 unit horizontally to find your next point.- Connect these points using a straight line. This line should extend infinitely in both directions, though practically we’ll stop where our data is relevant.Creating this visual helps in understanding how changes in length affect weight. It's a crucial skill for analyzing relationships in linear equations.

The substitution method is immensely helpful in solving problems that require finding the value of one variable when the other is known. Here, it's used to find the expected weight of an 80-ft blue whale using the given equation \( W = 3.51L - 192 \).- First, **substitute** the given length, 80 ft, into the equation in place of \( L \).- Perform the calculation: \( W = 3.51 \times 80 - 192 \). Breaking it down step by step makes it easier. First, multiply 3.51 by 80, getting 280.8.- Then subtract 192 from 280.8 to solve for \( W\). The result is 88.8.By substituting and simplifying, you determine that an 80-ft blue whale would weigh approximately 88.8 British tons. This method provides a precise solution, leveraging known quantities to find unknowns.