Use the image to answer the question.

Question

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 3 to 3 in one unit increments. The y-axis ranges from negative 3 to 6 in one unit increments. A downward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 1 comma 4 right parenthesis and left parenthesis 1 comma 0 right parenthesis.

Write the equation of the linear function shown on the graph.

A. y=2x−2

B. y=2x+2

C. y=−2x−2

D. y=−2x+2

Answer 1

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