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 plus 2

y=2x−2
y equals 2 x minus 2

y=−2x−2
y equals negative 2 x minus 2

y=2x+2

Answer 1

To find the equation of the linear function that passes through the points \((-1, 4)\) and \((1, 0)\), we can follow these steps:

1. Find the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let \((x_1, y_1) = (-1, 4)\) and \((x_2, y_2) = (1, 0)\): \[ m = \frac{0 - 4}{1 - (-1)} = \frac{-4}{2} = -2 \]

2. Use the point-slope form of the linear equation \(y - y_1 = m(x - x_1)\). Using point \((-1, 4)\): \[ y - 4 = -2(x + 1) \]

3. Expand and simplify: \[ y - 4 = -2x - 2 \] \[ y = -2x + 2 \]

Now we see that the equation of the line is: \[ y = -2x + 2 \]

Thus, the correct response is: y = -2x + 2