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 is
3 answers
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Question
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 2 comma 1 right parenthesis, left parenthesis 4 comma 2 right parenthesis, left parenthesis 6 comma 3 right parenthesis, and left parenthesis 8 comma 4 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 4 comma 0 right parenthesis, and left parenthesis 4 comma 2 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 4 comma 2 right parenthesis, left parenthesis 8 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis. The base is labeled as 4, and the perpendicular height on the right is labeled as 2.
Use similar triangles to determine the slope of the line. Write your answer in fraction form.
(1 point)
The slope is
.
slope = change in y / change in x
In the first triangle, the change in y is 2 and the change in x is 4. Therefore, the slope of the line for the first triangle is 2/4 = 1/2.
In the second triangle, the change in y is also 2 and the change in x is 4. Therefore, the slope of the line for the second triangle is also 2/4 = 1/2.
Since the line passes through these two triangles, the slope of the line is the same as the slope of both triangles, which is 1/2.