To find the equation of the linear function shown on the graph, we need to determine the slope and y-intercept.
The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Given the two points ( -1,4) and (1,0), we have:
m = (0 - 4) / (1 - (-1))
= -4 / 2
= -2
The y-intercept can be found by substituting one of the points into the equation y = mx + b and solving for b. Let's use the point (-1,4):
4 = -2(-1) + b
4 = 2 + b
b = 4 - 2
b = 2
Therefore, the equation of the linear function shown on the graph is:
y = -2x + 2
So, the correct answer is:
y=−2x+2