Question
Graphing Linear Equations Unit Test
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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 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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9 of 189 of 18 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 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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Answers
GPT-4o mini
To find the slope of the line using the given points, we can use the formula for slope (m):
\[
m = \frac{\text{change in } y}{\text{change in } x}
\]
From the points provided:
1. The coordinates of the points are:
- (0, 0)
- (1, 3)
- (2, 6)
- (3, 9)
Let's choose two points to calculate the slope. Using the points (1, 3) and (3, 9):
- Change in \(y\):
\[
9 - 3 = 6
\]
- Change in \(x\):
\[
3 - 1 = 2
\]
Now, we can substitute these values into the slope formula:
\[
m = \frac{6}{2} = 3
\]
Therefore, **the slope of the line is 3**.
\[
m = \frac{\text{change in } y}{\text{change in } x}
\]
From the points provided:
1. The coordinates of the points are:
- (0, 0)
- (1, 3)
- (2, 6)
- (3, 9)
Let's choose two points to calculate the slope. Using the points (1, 3) and (3, 9):
- Change in \(y\):
\[
9 - 3 = 6
\]
- Change in \(x\):
\[
3 - 1 = 2
\]
Now, we can substitute these values into the slope formula:
\[
m = \frac{6}{2} = 3
\]
Therefore, **the slope of the line is 3**.