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Question

Equations of Linear Functions Quick Check
5 of 55 of 5 Items

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 2 x plus 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 shown on the graph, we can use the two points the line passes through: \((-1, 4)\) and \((1, 0)\).

1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{1 - (-1)} = \frac{-4}{2} = -2 \]

2. Use the point-slope form of the equation: The point-slope form is given by \(y - y_1 = m(x - x_1)\). We can use one of the points, let's use \((1, 0)\): \[ y - 0 = -2(x - 1) \] \[ y = -2(x - 1) \] \[ y = -2x + 2 \]

Thus, the equation of the linear function shown on the graph is \(\mathbf{y = -2x + 2}\).

The correct response is: \(y = -2x + 2\).