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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
−
3
negative 3

−6
−
6
negative 6

−1

1 answer

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

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

Looking at the points given, we can use any two points on the line. Let's use the points (1, -3) and (3, -9):

  • \( y_2 = -9 \)
  • \( y_1 = -3 \)
  • \( x_2 = 3 \)
  • \( x_1 = 1 \)

Plugging these values into the slope formula:

\[ \text{slope} = \frac{-9 - (-3)}{3 - 1} = \frac{-9 + 3}{2} = \frac{-6}{2} = -3 \]

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