The correct response is:
A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: (0, 4), (1, 2), and (2, 0).
Use the table to answer the question.
x y
0 4
1 2
2 0
Graph the points in the coordinate plane from the data values in the table.
(1 point)
Responses
A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 4 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
Image with alt text: A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 4 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 1 right parenthesis, and left parenthesis 4 comma 0 right parenthesis.
Image with alt text: A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 2 right parenthesis, left parenthesis 2 comma 1 right parenthesis, and left parenthesis 4 comma 0 right parenthesis.
A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 2 right parenthesis, and left parenthesis 4 comma 0 right parenthesis.
Image with alt text: A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 2 right parenthesis, and left parenthesis 4 comma 0 right parenthesis.
A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 4 right parenthesis, left parenthesis negative 1 comma 2 right parenthesis, and left parenthesis negative 2 comma 0 right parenthesis.
Image with alt text: A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. The plotted points are as follows: left parenthesis 0 comma 4 right parenthesis, left parenthesis negative 1 comma 2 right parenthesis, and left parenthesis negative 2 comma 0 right parenthesis.
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11 answers
Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. One point is located in quadrant two and positioned at 1 increment along the x-axis and 6 increments along the y-axis. One point is located in quadrant 2 and positioned at 3 increments along the x-axis and 2 increments along the y-axis. One point is located in quadrant three and positioned at 5 increments along the x-axis and 2 increments along the y-axis.
Choose the ordered pairs that are plotted on this coordinate grid.
(1 point)
Responses
(−5, 2), (−3, 2), (−1, 6)
left parenthesis negative 5 comma 2 right parenthesis , left parenthesis negative 3 comma 2 right parenthesis , left parenthesis negative 1 comma 6 right parenthesis
(−5, −2), (−3, 2), (−1, 6)
left parenthesis negative 5 comma negative 2 right parenthesis , left parenthesis negative 3 comma 2 right parenthesis , left parenthesis negative 1 comma 6 right parenthesis
(−2, −5), (2, −3), (6, −1)
left parenthesis negative 2 comma negative 5 right parenthesis , left parenthesis 2 comma negative 3 right parenthesis , left parenthesis 6 comma negative 1 right parenthesis
(5, −2), (3, 2), (1, 6)
left parenthesis 5 comma negative 2 right parenthesis , left parenthesis 3 comma 2 right parenthesis , left parenthesis 1 comma 6 right parenthesis
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A coordinate plane shows four quadrants with both the x-axis and y-axis ranging from negative 10 to 10 in increments of 1. Three points are plotted. One point is located in quadrant two and positioned at 1 increment along the x-axis and 6 increments along the y-axis. One point is located in quadrant 2 and positioned at 3 increments along the x-axis and 2 increments along the y-axis. One point is located in quadrant three and positioned at 5 increments along the x-axis and 2 increments along the y-axis.
Choose the ordered pairs that are plotted on this coordinate grid.
(1 point)
Responses
(−5, 2), (−3, 2), (−1, 6)
left parenthesis negative 5 comma 2 right parenthesis , left parenthesis negative 3 comma 2 right parenthesis , left parenthesis negative 1 comma 6 right parenthesis
(−5, −2), (−3, 2), (−1, 6)
left parenthesis negative 5 comma negative 2 right parenthesis , left parenthesis negative 3 comma 2 right parenthesis , left parenthesis negative 1 comma 6 right parenthesis
(−2, −5), (2, −3), (6, −1)
left parenthesis negative 2 comma negative 5 right parenthesis , left parenthesis 2 comma negative 3 right parenthesis , left parenthesis 6 comma negative 1 right parenthesis
(5, −2), (3, 2), (1, 6)
left parenthesis 5 comma negative 2 right parenthesis , left parenthesis 3 comma 2 right parenthesis , left parenthesis 1 comma 6 right parenthesis
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The correct response is:
(5, −2), (3, 2), (1, 6)
(left parenthesis 5 comma negative 2 right parenthesis, left parenthesis 3 comma 2 right parenthesis, left parenthesis 1 comma 6 right parenthesis)
(5, −2), (3, 2), (1, 6)
(left parenthesis 5 comma negative 2 right parenthesis, left parenthesis 3 comma 2 right parenthesis, left parenthesis 1 comma 6 right parenthesis)
Review of the Coordinate Plane & Slope Quick Check
3 of 53 of 5 Items
Question
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
2
2
−12
negative Start Fraction 1 over 2 End Fraction
12
Start Fraction 1 over 2 End Fraction
4
4
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page 22 of 22
3 of 53 of 5 Items
Question
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
2
2
−12
negative Start Fraction 1 over 2 End Fraction
12
Start Fraction 1 over 2 End Fraction
4
4
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page 22 of 22
To find the slope of a line, we use the formula:
slope = (change in y)/(change in x)
In this case, the two plotted points are (-8, 0) and (0, 4).
Change in y = 4 - 0 = 4
Change in x = 0 - (-8) = 8
Thus, the slope of the line is:
slope = 4/8 = 1/2
Therefore, the correct response is:
-12
negative Start Fraction 1 over 2 End Fraction
slope = (change in y)/(change in x)
In this case, the two plotted points are (-8, 0) and (0, 4).
Change in y = 4 - 0 = 4
Change in x = 0 - (-8) = 8
Thus, the slope of the line is:
slope = 4/8 = 1/2
Therefore, the correct response is:
-12
negative Start Fraction 1 over 2 End Fraction
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
−1
negative 1
−56
negative Start Fraction 5 over 6 End Fraction
−5
negative 5
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page 22 of 22
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
−1
negative 1
−56
negative Start Fraction 5 over 6 End Fraction
−5
negative 5
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page 22 of 22
To find the slope of a line, we use the formula:
slope = (change in y)/(change in x)
In this case, the two plotted points are (-3, 1) and (2, -4).
Change in y = -4 - 1 = -5
Change in x = 2 - (-3) = 5
Thus, the slope of the line is:
slope = -5/5 = -1
Therefore, the correct response is:
-1
slope = (change in y)/(change in x)
In this case, the two plotted points are (-3, 1) and (2, -4).
Change in y = -4 - 1 = -5
Change in x = 2 - (-3) = 5
Thus, the slope of the line is:
slope = -5/5 = -1
Therefore, the correct response 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 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.
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.
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.
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.
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.
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Responses
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.
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.
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.
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.
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.
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The correct response is:
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.
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.
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.
To find the slope of a line, we use the formula:
slope = (change in y)/(change in x)
In this case, the two plotted points are (-6, 2) and (-4, 6).
Change in y = 6 - 2 = 4
Change in x = -4 - (-6) = 2
Thus, the slope of the line is:
slope = 4/2 = 2
Therefore, the slope of the line given its graph is 2.
slope = (change in y)/(change in x)
In this case, the two plotted points are (-6, 2) and (-4, 6).
Change in y = 6 - 2 = 4
Change in x = -4 - (-6) = 2
Thus, the slope of the line is:
slope = 4/2 = 2
Therefore, the slope of the line given its graph is 2.