Equations of Linear Functions Quick Check

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Question
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 minus 2

y=2x+2
y equals 2 x plus 2

y=2x−2
y equals 2 x minus 2

y=−2x+2
y equals negative 2 x plus 2
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Answer 1

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