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 equals negative 2 x minus 2

y=2x−2
y equals 2 x minus 2

y=−2x+2
y equals negative 2 x plus 2

y=2x+2

Answer 1

To find the equation of the linear function represented by the line passing through the points \((-1, 4)\) and \( (1, 0)\), we first need to determine the slope \(m\) of the line.

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the points \((-1, 4)\) and \((1, 0)\):

• \(x_1 = -1\), \(y_1 = 4\)
• \(x_2 = 1\), \(y_2 = 0\)

Plugging in these values:

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

Now, we have the slope \(m = -2\).

Next, we use the point-slope form of the equation of a line, which is:

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

Using the point \((1, 0)\):

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

Simplifying this gives:

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

\[ y = -2x + 2 \]

So the equation of the linear function is:

\[ y = -2x + 2 \]

Thus, the correct response is:

y = -2x + 2