Question

use the drawing tools) to form the correct answers on the provided graph.
a barrel in jays yard contains 80 gallons of water. water leaks out of the barrel at a rate of 1 gallon every 10 minutes.
under and graph the correct set of the equation for the gallons of water, y, remaining in the barrel in terms of the number of minutes elapsed, x.

Explanation:

Step1: Determine the equation

The initial amount of water \( y_0 = 80 \) gallons. The rate of decrease is \( \frac{1}{10} \) gallons per minute (since 1 gallon every 10 minutes). So the equation is \( y = 80 - \frac{1}{10}x \).

Step2: Find two points

• When \( x = 0 \), \( y = 80 \) (y - intercept).
• When \( y = 0 \), \( 0 = 80 - \frac{1}{10}x \Rightarrow \frac{1}{10}x = 80 \Rightarrow x = 800 \) (x - intercept).

Step3: Graph the line

Plot the points (0, 80) and (800, 0), then draw a line through them. The line should have a negative slope of \( -\frac{1}{10} \), starting at (0, 80) and decreasing towards (800, 0) as \( x \) (minutes) increases.

Answer:

The equation is \( y = 80 - \frac{1}{10}x \), and the graph is a line connecting (0, 80) and (800, 0) with a slope of \( -\frac{1}{10} \).