To model the relationship between the number of meals dispensed (x) and the amount of pet food remaining (y) using a linear function in slope-intercept form \( y = mx + b \), we need to determine the slope (m) and the y-intercept (b) based on the data you've provided.
From your data, we have the following points:
- Meal 1: (1, 25)
- Meal 2: (3, 17)
- Meal 3: (9, 7)
- Calculate the Slope (m)
We can use two points to calculate the slope. Let's use the first two points (1, 25) and (3, 17).
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (1, 25)\) and \((x_2, y_2) = (3, 17)\):
\[ m = \frac{17 - 25}{3 - 1} = \frac{-8}{2} = -4 \]
- Find the y-intercept (b)
Using the slope-intercept form \( y = mx + b \), we can substitute one of the points into the equation to find \( b \). We'll use the point (1, 25):
\[ 25 = -4(1) + b \] \[ 25 = -4 + b \] \[ b = 25 + 4 = 29 \]
- Write the Linear Function
Now we have the slope \( m = -4 \) and the y-intercept \( b = 29 \). Thus, the equation that models the situation is:
\[ y = -4x + 29 \]
So the function rule in slope-intercept form is:
\[ y = -4x + 29 \]