The table below shows the relationship between the number of teaspoons of baking powder in a mix and the height of fudge brownies in centimeters. Which equation represents the height of fudge brownies with x teaspoons of baking powder?

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).

1. The formula for the slope \(m\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points:
- \(y_2 = 2.99\), \(y_1 = 2.15\)
- \(x_2 = 8\), \(x_1 = 5\)

\[
m = \frac{2.99 - 2.15}{8 - 5} = \frac{0.84}{3} = 0.28
\]

2. 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 **: \( y = 0.28x + 0.75\).