The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.

Question

A graph titled Water Supply with number of days on the x-axis and gallons of water left on the y-axis. A line goes through points (6, 33) and (15, 15).

What is the slope of the line?
–2
Negative one-half
StartFraction 7 Over 16 EndFraction
StartFraction 39 Over 30 EndFraction

Answer 1

To find the slope of the line that passes through the points \((6, 33)\) and \((15, 15)\), we can use the formula for the slope \(m\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where \((x_1, y_1) = (6, 33)\) and \((x_2, y_2) = (15, 15)\).

Now substituting the values into the formula:

\[ m = \frac{15 - 33}{15 - 6} \]

Calculating the numerator and denominator:

\[ m = \frac{-18}{9} = -2 \]

Thus, the slope of the line is \(-2\).