Use the image to answer the 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.
(1 point)
Responses
y=−2x+2
y equals negative 2 x plus 2
y=2x−2
y equals 2 x minus 2
y=−2x−2
y equals negative 2 x minus 2
y=2x+2
y equals 2 x plus 2
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To find the equation of the linear function shown on the graph, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) of the line using the two plotted points: (-1, 4) and (1, 0).
m = (y2 - y1) / (x2 - x1)
= (0 - 4) / (1 - (-1))
= -4 / 2
= -2
Now that we know the slope is -2, we can substitute it into the slope-intercept form:
y = -2x + b
To find the y-intercept (b), we can substitute the coordinates of one of the plotted points into the equation. Let's use the point (-1, 4):
4 = -2(-1) + b
4 = 2 + b
4 - 2 = b
2 = b
Now we have the value of b, which is 2. So the equation of the linear function shown on the graph is:
y = -2x + 2
Therefore, the correct answer is: y=−2x+2.