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 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 point)
The slope is
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To determine the slope of the line, we can use the concept of similar triangles.
In the first triangle, the base is labeled as 1 and the perpendicular height on the right is labeled as 3.
In the second triangle, the base is labeled as 2 and the perpendicular height on the right is labeled as 6.
Since the triangles are similar, we can set up the following proportion:
(base of first triangle) / (perpendicular height of first triangle) = (base of second triangle) / (perpendicular height of second triangle)
Substituting the given values, we get:
1/3 = 2/6
To simplify the proportion, we can cross-multiply:
6 * 1 = 3 * 2
6 = 6
Since both sides of the equation are equal, this means that the proportion is true.
Therefore, we can conclude that the slope of the line is 1/3.