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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
y equals negative 2 x minus 2
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Answer 1

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

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

Substituting in the coordinates of the points:

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

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

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

We can use either of the two points; let's use \((1, 0)\):

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

Simplifying this:

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

Thus, the equation of the linear function is:

\[ y = -2x + 2 \]

So the correct response is:

y = −2x + 2