Question

card 16
a container releases fuel at a rate of 5 gallons per second. the variable y represents the amount of fuel remaining in the container and x represents the number of seconds that have passed since the fuel started dispensing.
which line could represent this situation?
explain your thinking.

Explanation:

Step1: Analyze the relationship

The fuel remaining \( y \) decreases as time \( x \) (seconds) increases because fuel is being released. So the line should have a negative slope.

Step2: Identify the line

Among the lines \( l \), \( m \), and \( r \), line \( r \) has a negative slope (it's decreasing from left to right), while \( l \) has a positive slope (increasing) and \( m \) has a slope of 0 (horizontal). So line \( r \) represents the situation where fuel remaining decreases over time as seconds pass.

Answer:

The line \( r \) (the line with negative slope, decreasing from left to right) could represent this situation because the amount of fuel remaining (\( y \)) should decrease as the number of seconds (\( x \)) increases (since fuel is being released at a constant rate), and line \( r \) has a negative slope indicating a decreasing relationship between \( x \) and \( y \).