To find the equation that represents the height of the brownies based on the number of teaspoons of baking powder, we can use the two-point form of the linear equation \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
First, we will calculate the slope \(m\) using two points from the table. For example, let's use the points (5, 2.15) and (8, 2.99).
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The formula for the slope \(m\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]Substituting the points:
- \(y_2 = 2.99\), \(y_1 = 2.15\)
- \(x_2 = 8\), \(x_1 = 5\)
\[ m = \frac{2.99 - 2.15}{8 - 5} = \frac{0.84}{3} = 0.28 \]
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Now, we can use one of the points to find \(b\). We can use the point (5, 2.15):
\[ y = mx + b \ 2.15 = 0.28(5) + b \ 2.15 = 1.4 + b \ b = 2.15 - 1.4 = 0.75 \]
Now we have \(m = 0.28\) and \(b = 0.75\). Thus, the equation representing the height \(y\) of the brownies with \(x\) teaspoons of baking powder is:
\[ y = 0.28x + 0.75 \]
This matches option A: \( y = 0.28x + 0.75\).
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