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.

(1 point)
Responses

y=−2x−2
y
=
−
2
x
−
2
y equals negative 2 x minus 2

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

y=2x−2
y
=
2
x
−
2
y equals 2 x minus 2

y=−2x+2

Answer 1

To determine the equation of the linear function that passes through the points (-1, 4) and (1, 0), we can calculate the slope (m) first using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (-1, 4) as \((x_1, y_1)\) and (1, 0) as \((x_2, y_2)\):

\[ m = \frac{0 - 4}{1 - (-1)} = \frac{-4}{2} = -2 \]

Now that we have the slope \(m = -2\), we can use the point-slope form of the equation of a line, which is:

\[ y - y_1 = m(x - x_1) \]

Let's use the point (1, 0):

\[ y - 0 = -2(x - 1) \] \[ y = -2x + 2 \]

Thus, the equation of the line is:

\[ y = -2x + 2 \]

So the correct response is:

y = -2x + 2