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 five 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 2 right parenthesis, left parenthesis 2 comma 4 right parenthesis, left parenthesis 3 comma 6 right parenthesis, and left parenthesis 4 comma 8 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 3 comma 0 right parenthesis, and left parenthesis 3 comma 6 right parenthesis. The base is labeled as 3, and the perpendicular height on the right is labeled as 6. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 3 comma 6 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 2.

Use similar triangles to determine the slope of the line.

(1 point)

The slope of the line can be determined by using the formula:

slope = change in y-coordinates / change in x-coordinates.

In the given image, we can observe that the change in y-coordinates from (0,0) to (3,6) is 6 and the change in x-coordinates is 3. Therefore, the slope of the line is:

slope = 6/3 = 2.

To determine the slope of the line, we can compare the ratios of the vertical change to the horizontal change for the similar triangles formed by the line and the two triangles.

The first triangle has a base of 3 and a perpendicular height of 6. Therefore, the slope of the line segment between the points (0, 0) and (3, 6) is:

Slope of line segment = vertical change / horizontal change
= 6 / 3
= 2

The second triangle has a base of 1 and a perpendicular height of 2. Therefore, the slope of the line segment between the points (3, 6) and (4, 8) is:

Slope of line segment = vertical change / horizontal change
= 2 / 1
= 2

Since the ratios of vertical change to horizontal change for both line segments are the same, we can conclude that the slope of the line is 2.