To write an equation that represents the relationship between the time in minutes (x) and the gallons of gas in the truck (y), we need to determine the rate of gas that is filled per minute.
From the points provided on the graph, we can calculate the rate of change of gallons of gas per minute. We have the points (4, 72) and (10, 144):
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The change in gallons of gas from 4 to 10 minutes is: \( 144 - 72 = 72 \) gallons.
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The change in time from 4 to 10 minutes is: \( 10 - 4 = 6 \) minutes.
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Therefore, the rate of gas being added per minute is: \( \frac{72 \text{ gallons}}{6 \text{ minutes}} = 12 \text{ gallons per minute} \).
Now, we can express the relationship with an equation. To find the equation in slope-intercept form, we start with: \[ y = mx + b \] where \( m \) is the slope (12 gallons per minute) and \( b \) is the initial amount of gas in the truck (which we'll denote as \( b \)).
To find \( b \), we can use one of the points given. Using the point (4, 72): \[ 72 = 12(4) + b \] \[ 72 = 48 + b \] \[ b = 72 - 48 \] \[ b = 24 \]
Thus, the equation representing the situation is: \[ y = 12x + 24 \]
Predictions:
Now we can analyze the points (4, 72) and (10, 144):
- The point (4, 72) means that after 4 minutes, there are 72 gallons of gas in the truck.
- The point (10, 144) means that after 10 minutes, there are 144 gallons of gas in the truck.
Summary:
- (4, 72) indicates that after 4 minutes, the amount of gas in the truck is 72 gallons.
- (10, 144) indicates that after 10 minutes, the amount of gas in the truck is 144 gallons.