Write the equation of the linear function shown on the graph. (-1,4) (1,0) (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 linear function that passes through the points (-1, 4) and (1, 0), we first need to calculate the slope (m) using the slope formula:

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

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

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

Now that we know the slope is -2, we can 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, we get:

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

So, the equation of the line is:

\[ y = -2x + 2 \]

Therefore, the correct response from the options provided is:

y = -2x + 2.