To find the equation of the linear function, we need to determine the slope and the y-intercept of the line.
First, calculate the slope using the two points provided: (−1, 4) and (1, 0).
m = (0 - 4) / (1 - (-1))
m = -4 / 2
m = -2
Now that we have the slope, we need to find the y-intercept. We can use one of the points to substitute into the equation y = mx + b.
Using the point (1, 0):
0 = -2(1) + b
0 = -2 + b
b = 2
Therefore, the equation of the linear function shown on the graph is:
y = -2x + 2
Therefore, the correct answer is:
D. y=−2x+2