Question

There are approximately 126 calories in a 2 ounce serving of lean hamburger and approximately 189 calories in a 3 ounce serving. a. Determine a linear function for the number of calories y in Lear hamburger in terms of the size of the serving x. b. Use your function to estimate the number of Calories in a 9- ounce serving of lean hamburger

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Hermann

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To find the linear function, we start by identifying the slope \(m\) using the two given points: \( (2, 126) \) and \( (3, 189) \).

1. Calculate the slope \( m \):

m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{189 - 126}{3 - 2} = \frac{63}{1} = 63

2. With the slope known, use point-slope form to write the equation of the line. Using the point \( (2, 126) \):

y - 126 = 63(x - 2)

3. Simplify to find the equation:

y - 126 = 63x - 126

y = 63x

Now, use this equation to find the calories for a 9-ounce serving:

4. Substitute \( x = 9 \) into the equation:

y(9) = 63 \cdot 9 = 567

Thus, the number of calories in a 9-ounce serving is 567 calories.

1. Calculate the slope \( m \):

2. With the slope known, use point-slope form to write the equation of the line. Using the point \( (2, 126) \):

3. Simplify to find the equation:

Now, use this equation to find the calories for a 9-ounce serving:

4. Substitute \( x = 9 \) into the equation:

Thus, the number of calories in a 9-ounce serving is 567 calories.

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