Question

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**.