Use the image to answer the question.

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 1 comma negative 3 right parenthesis, left parenthesis 2 comma negative 6 right parenthesis, and left parenthesis 3 comma negative 9 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 1 comma 0 right parenthesis, and left parenthesis 1 comma negative 3 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 3. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 3 comma negative 3 right parenthesis, and left parenthesis 3 comma negative 9 right parenthesis. The base is labeled as 2, and the perpendicular height on the right is labeled as 6.

What is the slope of the line?

(1 point)
Responses

3
3

−3
negative 3

−6
negative 6

−1

Answer 1

To find the slope of the line, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Using the points \((0, 0)\) and \((1, -3)\):

• \(x_1 = 0\), \(y_1 = 0\)
• \(x_2 = 1\), \(y_2 = -3\)

Plugging these values into the slope formula gives:

\[ m = \frac{-3 - 0}{1 - 0} = \frac{-3}{1} = -3 \]

Thus, the slope of the line is \(-3\).

So, the correct response is:

−3