Question

santiago buys a container of milk to make atole. the cups of milk left in the container, y, is a linear function of the number of batches he makes, x. the graph of the function passes through the points (1,12) and (3,4). find and describe the rate of change of the function. the rate of change is -4. it represents a decrease in the amount of milk in the container for each batch of atole made. find and describe the initial value of the function. the initial value is

Explanation:

Step1: Find the equation of the line

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We already know $m=-4$ (from the rate of change). Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(1,12)$ and $m = - 4$.
$y-12=-4(x - 1)$

Step2: Expand and solve for $y$

$y-12=-4x + 4$. Add 12 to both sides of the equation:
$y=-4x+16$
The initial value is the value of $y$ when $x = 0$. Substitute $x = 0$ into $y=-4x + 16$.
$y=16$

Answer:

16