Bot GPT 4-o mini To write a function in slope-intercept form (\(y = mx + b\)), we need to identify the slope (\(m\)) and the y-intercept (\(b\)).
Since I don't have the actual data from the table you mentioned, let's outline the steps you would typically follow to derive this rule:
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Identify Points from the Table: Look for at least two data points in the table that represent the number of meals dispensed (\(x\)) and the amount of pet food remaining (\(y\)) in cups.
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Calculate the Slope (\(m\)): Use the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \((x_1, y_1)\) and \((x_2, y_2)\) are two points from the table.
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Find the y-Intercept (\(b\)): The y-intercept is the value of \(y\) when \(x = 0\). If the table includes a point where \(x = 0\), you can use that directly. Otherwise, you can use the slope and one of the points to find it using: \[ b = y - mx \]
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Write the Function: Once you have \(m\) and \(b\), plug these values into the slope-intercept form: \[ y = mx + b \]
Example
Assuming from the table you found these points:
- Point 1: (1, 8) → After 1 meal, 8 cups remain.
- Point 2: (3, 4) → After 3 meals, 4 cups remain.
Calculate the slope (\(m\)): \[ m = \frac{4 - 8}{3 - 1} = \frac{-4}{2} = -2 \]
Next, use one of the points to find the intercept (\(b\)): Using point (1, 8): \[ 8 = -2(1) + b \implies 8 = -2 + b \implies b = 10 \]
Now you can write the function: \[ y = -2x + 10 \]
This formula indicates that for each meal dispensed, 2 cups of food are used, starting from 10 cups.
If you provide the specific data from your table, I can help you derive the function rule directly!
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