To find the equation of the linear function that models the given points \((0, 20)\), \((10, 22.5)\), and \((20, 25)\), we can start by calculating the slope of the line using two of the points.
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the points \((0, 20)\) and \((10, 22.5)\):
\[ m = \frac{22.5 - 20}{10 - 0} = \frac{2.5}{10} = 0.25 \]
Now, we have the slope \(m = 0.25\). Next, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Using the point \((0, 20)\):
\[ y - 20 = 0.25(x - 0) \]
Simplifying this, we get:
\[ y - 20 = 0.25x \] \[ y = 0.25x + 20 \]
Now, we can confirm that this equation matches the remaining points. Let's check point \((10, 22.5)\):
\[ y = 0.25(10) + 20 = 2.5 + 20 = 22.5 \]
And now check point \((20, 25)\):
\[ y = 0.25(20) + 20 = 5 + 20 = 25 \]
Both points satisfy the equation.
Thus, the equation of the linear function that models the graph is:
\[ y = 0.25x + 20 \]
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