Slope as Unit Rate Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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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
.
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To determine the slope of the line, we can use the formula:
slope = (change in y)/(change in x)
Looking at the two triangles, we can see that they are similar. This means that the ratio of their corresponding sides is the same.
In the first triangle, the base is 4 and the perpendicular height is 2. In the second triangle, the base is also 4 and the perpendicular height is also 2.
So, the change in y is 2 and the change in x is 4.
Therefore, the slope of the line is:
slope = 2/4 = 1/2
To determine the slope of the line, we can use the concept of similar triangles.
In the first triangle, the base is labeled as 4 and the perpendicular height on the right is labeled as 2. In the second triangle, the base is also labeled as 4 and the perpendicular height on the right is also labeled as 2.
Since the triangles are similar, the ratios of corresponding side lengths are equal. Therefore, the ratio of the vertical side lengths (perpendicular heights) in both triangles is the same.
So, the slope of the line can be calculated as the ratio of the change in y-coordinates to the change in x-coordinates between any two points on the line.
Let's take the points (0, 0) and (8, 4) to calculate the slope:
Change in y-coordinates = 4 - 0 = 4
Change in x-coordinates = 8 - 0 = 8
So, the slope is 4/8.
Simplifying the fraction, we get the final answer:
The slope is 1/2.