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 3 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 3 comma 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 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 3 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The base is labeled as 2, and the perpendicular height on the right is labeled as 6.

Use similar triangles to determine the slope of the line.

(1 poin t)
The slope is
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Answer 1

To determine the slope of the line using similar triangles, we need to analyze the relationship between the base and height of each triangle formed by the line.

1. First Triangle:
   • Base: 1 unit (from (0,0) to (1,0))
   • Height: 3 units (from (1,0) to (1,3))
   • This triangle has a vertical height of 3 above its base.

The slope derived from this triangle is given by: \[ \text{slope} = \frac{\text{height}}{\text{base}} = \frac{3}{1} = 3 \]

2. Second Triangle:
   • Base: 2 units (from (1,3) to (3,3))
   • Height: 6 units (from (3,3) to (3,9))
   • This triangle has a vertical height of 6 above its base.

The slope derived from this triangle is given by: \[ \text{slope} = \frac{\text{height}}{\text{base}} = \frac{6}{2} = 3 \]

In both cases, the slope of the line is consistently calculated as 3.

Therefore, the slope of the line is 3.