Question

1. hanna works at an aquarium and needs to drain the seahorse tank for cleaning. the gallons of water in the tank based on the number of minutes it has been draining is shown in the table below.

what is the slope?
what does the slope represent in the situation?
what is the y - intercept?
what does the y - intercept represent in the situation?
equation:

x minutes	0	4	8	12

Explanation:

Step1: Calculate slope using two points

Use points $(0,60)$ and $(4,50)$. Slope formula: $\frac{y_2-y_1}{x_2-x_1} = \frac{50-60}{4-0} = -\frac{10}{4} = -\frac{5}{2}$

Step2: Interpret the slope

Slope is change in y (gallons) over change in x (minutes), so it is the rate the tank drains, $-\frac{5}{2}$ gallons per minute.

Step3: Identify y-intercept

y-intercept is y-value when $x=0$, from table it is 60.

Step4: Interpret the y-intercept

When $x=0$ (0 minutes draining), the tank has 60 gallons, the initial amount.

Step5: Write linear equation

Use slope-intercept form $y=mx+b$, substitute $m=-\frac{5}{2}$, $b=60$: $y = -\frac{5}{2}x + 60$

Answer:

1. Slope: $-\frac{5}{2}$
2. Slope representation: Rate of water drainage (gallons per minute)
3. y-intercept: 60
4. y-intercept representation: Initial gallons of water
5. Equation: $y = -\frac{5}{2}x + 60$