To find the equation of the linear function shown on the graph with points \((-1, 4)\) and \((1, 0)\), we can start by calculating the slope \(m\) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((x_1, y_1) = (-1, 4)\) and \((x_2, y_2) = (1, 0)\):
\[
m = \frac{0 - 4}{1 - (-1)} = \frac{-4}{2} = -2
\]
Now that we have the slope \(m = -2\), we can use the point-slope form of a linear equation, which is:
\[
y - y_1 = m(x - x_1)
\]
Using the point \((1, 0)\):
\[
y - 0 = -2(x - 1)
\]
Simplifying this:
\[
y = -2x + 2
\]
Thus, the equation of the linear function is:
\[
y = -2x + 2
\]
The correct response is:
**y = −2x + 2** (y equals negative 2 x plus 2)