Question

a is cleaning her fish tank. she starts with a full tank of water, and as she uses a siphon to drain the water, the level gradually decreases. the graph represents the relationship between y, the amount of water left in the tank, and x, the number of hours she spends siphoning the water out. which equation best represents the relationship? a. y = 20x + 50 b. y = -2x + 50 c. y = -50x + 10 d. y = -10x + 50

Explanation:

Step1: Identify the slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Determine the y - intercept

When $x = 0$ (at the start, before any water is siphoned), the tank is full. From the graph, when $x = 0$, $y=50$, so $b = 50$.

Step3: Calculate the slope

The line passes through points $(0,50)$ and $(5,0)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 50}{5-0}=\frac{-50}{5}=- 10$.

Step4: Find the equation

Substitute $m=-10$ and $b = 50$ into $y=mx + b$, we get $y=-10x + 50$.

Answer:

D. $y=-10x + 50$