Question

Use the image to answer the question.

An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through four plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 4 comma negative 4 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis. The base is labeled as 2, and the perpendicular height on the left is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 2 comma negative 6 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The base is labeled as 4, and the perpendicular height on the left is labeled as 4.

What is the slope of the line?

(1 point)
Responses

−2
negative 2

−1
negative 1

2
2

1

Answer 1

To find the slope of the line passing through the points (0, 0), (2, -2), (4, -4), and (6, -6), we can use the formula for the slope (m) between two points (x1, y1) and (x2, y2):

\[
m = \frac{y2 - y1}{x2 - x1}
\]

Using the points (0, 0) and (2, -2):

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

We can also check with another pair of points, such as (2, -2) and (4, -4):

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

In both cases, the slope is consistent.

Therefore, the slope of the line is \(-1\).

The correct response is:
−1