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 2 x plus 2

y=−2x+2

Answer 1

To find the equation of the line that passes through the points \((-1, 4)\) and \((1, 0)\), we can use the slope-intercept form of a linear equation, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

1. Calculate the slope (m): The formula for the slope \(m\) 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 \((1, 0)\):

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

2. Use the slope to find the y-intercept (b): We can use one of the points to find \(b\). Let's use the point \((1, 0)\):

   \[ 0 = -2(1) + b \]

   \[ 0 = -2 + b \]

   \[ b = 2 \]

3. Write the equation of the line: Now that we have \(m = -2\) and \(b = 2\), the equation of the line is:

   \[ y = -2x + 2 \]

Therefore, the correct option is:

y = −2x + 2.