Monica has 4 pounds of sweet potatoes. joey eats 1 pound every 2 hours write and graph an equation in slope intersept form for this situation
To model the situation where Joey eats sweet potatoes over time, we first need to establish our variables and create an equation.
1. **Define the variables:**
- Let \( x \) represent the number of hours that have passed.
- Let \( y \) represent the amount of sweet potatoes (in pounds) remaining.
2. **Initial conditions and rate of consumption:**
- Monica starts with 4 pounds of sweet potatoes.
- Joey eats 1 pound every 2 hours, which means the rate at which he will eat is \( \frac{1}{2} \) pounds per hour.
3. **Equation:**
Since Joey is consuming the sweet potatoes, the amount remaining decreases over time. Thus, the relationship can be expressed as:
\[
y = -\frac{1}{2}x + 4
\]
This is in slope-intercept form \( y = mx + b \), where:
- \( m = -\frac{1}{2} \) (the slope, which indicates the rate of consumption)
- \( b = 4 \) (the y-intercept, which indicates the starting amount of sweet potatoes)
4. **Graphing the equation:**
- Start by plotting the y-intercept, which is the point (0, 4).
- The slope of \( -\frac{1}{2} \) means that for each hour that passes, the amount of sweet potatoes decreases by half a pound. Therefore, after 2 hours (1 unit along the x-axis), the amount will decrease by 1 pound.
- Plot another point: at \( x = 2 \), \( y = -\frac{1}{2}(2) + 4 = 3 \), giving point (2, 3).
- Continue plotting points like (4, 2) and (6, 0).
- Remember to indicate that Joey cannot eat more than the initial 4 pounds, hence, the graph will not extend below the x-axis.
5. **Graph:**
The graph will start at the point (0, 4) and decrease linearly due to the negative slope of \(-\frac{1}{2}\). The line will cross the x-axis when there are no sweet potatoes left.
Here's a sketch of the graph:
```
| y (pounds)
|
| 4 * (0, 4)
| |
| 3 * (2, 3)
| |
| 2 * (4, 2)
| |
| 1 * (6, 0)
| |
|____________________________ x (hours)
0 1 2 3 4 5 6
```
In conclusion, the equation representing the situation is \( y = -\frac{1}{2}x + 4 \), and the graph decreases linearly until it reaches the x-axis at 6 hours.