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 2 x minus 2
y=2x+2
y equals 2 x plus 2
y=−2x+2
y equals negative 2 x plus 2
y=−2x−2
y equals negative 2 x minus 2
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Looking at the given points (-1, 4) and (1, 0), we can find the slope of the line passing through them using the formula:
m = (y2 - y1) / (x2 - x1)
m = (0 - 4) / (1 - (-1))
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to write the equation of the line. Using the point (-1, 4):
y - y1 = m(x - x1)
y - 4 = -2(x - (-1))
Simplifying:
y - 4 = -2(x + 1)
y - 4 = -2x - 2
y = -2x + 2 + 4
y = -2x + 6
Therefore, the equation of the linear function shown on the graph is y = -2x + 6.