- Filling out the table:
To find the values for \( y \) (the amount of food left) based on \( x \) (the number of days), we know that they consume 12 pounds of food per day.
The formula for food left is:
\[ y = \text{initial food} - \text{food consumed} \]
With \( y = 360 - 12x \):
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For \( x = 0 \): \[ y = 360 - 12(0) = 360 \]
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For \( x = 5 \): \[ y = 360 - 12(5) = 360 - 60 = 300 \]
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For \( x = 10 \): \[ y = 360 - 12(10) = 360 - 120 = 240 \]
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For \( x = 15 \): \[ y = 360 - 12(15) = 360 - 180 = 180 \]
So the table is:
| x | y | |-----|-----| | 0 | 360 | | 5 | 300 | | 10 | 240 | | 15 | 180 |
- The equation in slope-intercept form:
The slope-intercept form of a linear equation is given by:
\[ y = mx + b \]
Where \( m \) is the slope and \( b \) is the y-intercept.
Here, we can derive the equation:
- The y-intercept (when \( x = 0 \)) is \( b = 360 \).
- The slope \( m \) is the rate of food consumed per day, which is -12 (since food decreases).
So, the equation is:
\[ y = -12x + 360 \]
- In how many days will the hikers run out of food?
To find when they run out of food, we set \( y = 0 \):
\[ 0 = -12x + 360 \]
Now, solve for \( x \):
\[ 12x = 360 \] \[ x = \frac{360}{12} = 30 \]
The hikers will run out of food in 30 days.
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