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
given by the ratio of the change in y-coordinates to the change in x-coordinates.
In the first triangle, the change in y-coordinates is 3 and the change in x-coordinates is 1. Thus, the slope of the line segment between (0,0) and (1,3) is 3/1 or 3.
In the second triangle, the change in y-coordinates is 6 and the change in x-coordinates is 2. Thus, the slope of the line segment between (1,3) and (3,9) is 6/2 or 3.
Since both line segments have the same slope, we can conclude that the overall slope of the line passing through all four points is 3.