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 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 (0 , 0), (1, 0), and (1 , 3). 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 (1 , 3), (3 , 3), and (3 , 9). 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.
To determine the slope of the line, we can use the information about the triangles and their sides. In similar triangles, the ratio of corresponding sides is equal.
In the first triangle, the base is labeled as 1, and the perpendicular height on the right is labeled as 3. Therefore, the slope of the first triangle can be calculated as 3/1 = 3.
In the second triangle, the base is labeled as 2, and the perpendicular height on the right is labeled as 6. Therefore, the slope of the second triangle can be calculated as 6/2 = 3.
Since the line passes through the points (0, 0), (1, 3), (2, 6), and (3, 9), which are the vertices of the two triangles, and the slopes of the triangles are equal, we can conclude that the slope of the line is 3.