Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis negative 6 comma 2 right parenthesis, left parenthesis negative 4 comma 6 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
Find the slope of the line given its graph.
(1 point)
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To find the slope of the line, we need to determine the change in the y-coordinate divided by the change in the x-coordinate.
The first point is (-6, 2) and the second point is (-4, 6).
Using the formula for slope (m = (y2 - y1) / (x2 - x1)), we can substitute the coordinates into the formula:
m = (6 - 2) / (-4 - (-6))
m = (6 - 2) / (-4 + 6)
m = 4 / 2
m = 2
Therefore, the slope of the line is 2.
Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
Find the slope of the line given its graph.
(1 point)
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To find the slope of the line, we need to determine the change in the y-coordinate divided by the change in the x-coordinate.
The first point is (0, 2) and the second point is (1, -1).
Using the formula for slope (m = (y2 - y1) / (x2 - x1)), we can substitute the coordinates into the formula:
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Therefore, the slope of the line is -3.
Use the image to answer the question.
A downward-sloping diagonal line with arrows on both ends passes through quadrants 2 and 4. Three points are plotted and labeled on the line: left parenthesis negative 3 comma 1 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 3 comma negative 1 right parenthesis. Both the x-axis and y-axis range from negative 10 to 10 in increments of 1.
Find the slope of the line using similar triangles.
(1 point)
The slope is
.
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To find the slope of the line using similar triangles, we can choose two points on the line and form a right triangle with the x-axis.
Let's choose the points (-3, 1) and (0, 0) to form the right triangle. The vertical leg of the triangle is 1 unit and the horizontal leg is 3 units.
Since the line is downward-sloping, the slope will be negative.
To find the slope, we divide the change in the y-coordinate (-1) by the change in the x-coordinate (3):
slope = -1/3
Therefore, the slope of the line using similar triangles is -1/3.
Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis negative 8 comma 0 right parenthesis, left parenthesis 0 comma 4 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
Find the slope of the line given its graph.
(1 point)
Responses
4
4
12
Start Fraction 1 over 2 End Fraction
2
2
−12
negative Start Fraction 1 over 2 End Fraction
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To find the slope of the line, we need to determine the change in the y-coordinate divided by the change in the x-coordinate.
The first point is (-8, 0) and the second point is (0, 4).
Using the formula for slope (m = (y2 - y1) / (x2 - x1)), we can substitute the coordinates into the formula:
m = (4 - 0) / (0 - (-8))
m = 4 / 8
m = 1/2
Therefore, the slope of the line is 1/2.
Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis negative 3 comma 1 right parenthesis, left parenthesis 2 comma negative 4 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
Find the slope of the line given its graph.
(1 point)
Responses
1
1
−56
negative Start Fraction 5 over 6 End Fraction
−5
negative 5
−1
negative 1
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To find the slope of the line, we need to determine the change in the y-coordinate divided by the change in the x-coordinate.
The first point is (-3, 1) and the second point is (2, -4).
Using the formula for slope (m = (y2 - y1) / (x2 - x1)), we can substitute the coordinates into the formula:
m = (-4 - 1) / (2 - (-3))
m = -5 / 5
m = -1
Therefore, the slope of the line is -1.
Why can you use similar triangles to explain why the slope is the same between any two distinct points on a nonvertical line?(1 point)
Responses
The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.
The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.
In similar triangles, the change in y-values represents the run, and the change in x-values represents the rise of the line the triangles are placed against. So the ratio riserun can show that the slope is the same between any two points along the line.
In similar triangles, the change in y -values represents the run, and the change in x -values represents the rise of the line the triangles are placed against. So the ratio Start Fraction rise over run End Fraction can show that the slope is the same between any two points along the line.
The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line.
The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line.
The interior angles of similar triangles used at different points along the line can be added to measure the slope of the line. The corresponding angles of similar triangles are the same, so the slope can be shown as the same using any two points along the line.