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
The slope of the line is 2.
Slope as Unit Rate Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
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
.
To determine the slope of the line using the given information, we can use the formula:
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.
To determine the slope of the line, we can use the concept of similar triangles.
In the first triangle, the base (horizontal side) has a length of 3 units, and the perpendicular height (vertical side) has a length of 6 units.
In the second triangle, the base (horizontal side) has a length of 1 unit, and the perpendicular height (vertical side) has a length of 2 units.
Since both triangles are similar, their corresponding sides are proportional. This means that the ratio of the base length to the perpendicular height in the first triangle is the same as the ratio in the second triangle.
Therefore, the slope of the line can be determined by finding the ratio of the vertical change (perpendicular height) to the horizontal change (base) in either triangle.
In the first triangle, the ratio is 6/3 = 2.
Therefore, the slope of the line is 2.