Question

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Slope as Unit Rate Quick Check
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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

1
1

−2
negative 2

−1
negative 1

2

Answer 1

To determine the slope of the line passing through the points (0, 0) and (2, -2), we can use the formula for slope:

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

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

\[
y_1 = 0, \quad y_2 = -2, \quad x_1 = 0, \quad x_2 = 2
\]

Plugging in the values:

\[
\text{slope} = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1
\]

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

The correct response is:

**−1**