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
1

−1
negative 1

2
2
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Answer 1

To find the slope of the line, we can use the slope formula:

\[
\text{slope} (m) = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the points given, we can choose two points that lie on the line. The points \((0, 0)\) and \((2, -2)\) can be used for this calculation.

Let's assign:
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, -2) \)

Now substituting the values into the slope formula:

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

Thus, the slope of the line is:

\[
\boxed{-1}
\]