Question

this graph shows a tank filling with water over a period of time.
write the equation of the linear function shown on the graph
in slope intercept form.
$y = mx + b$
$y=\frac{1}{3}x + 3$
explain what the y - intercept means in the context of this
problem.

Explanation:

Step1: Find the slope ($m$)

The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Let's take two points on the line: $(0,3)$ and $(6,5)$.
$m=\frac{5 - 3}{6 - 0}=\frac{2}{6}=\frac{1}{3}$.

Step2: Identify the y - intercept ($b$)

The y - intercept is the value of $y$ when $x = 0$.
From the point $(0,3)$, we get $b = 3$.

Step3: Write the equation in slope - intercept form

Using $y=mx + b$, substitute $m=\frac{1}{3}$ and $b = 3$.
So, $y=\frac{1}{3}x+3$.

In the context of the problem, the y - intercept ($b = 3$) represents the initial volume of water in the holding tank. When $x = 0$ (at the start, i.e., time $t = 0$ hours), the volume of water in the tank is 3 gallons.

Answer:

The equation of the linear function is $y=\frac{1}{3}x + 3$. The y - intercept (3) means that initially (at time $x = 0$ hours), there are 3 gallons of water in the holding tank.