Use the table to answer the question.
x 3 4 5 6 7 8 9 10 11
y 3.5 4 4.2 4.5 4.8 5.5 5.8 6.4 6.7
Recognize which of the following graphs correctly uses a straight line to model the relationship between the quantitative variables in the table.
(1 point)
Responses
1. Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend linearly upward. An upward trend line is plotted and labeled y equals 0.35 times x plus 2.8. The line follows the slope of the points. The x-axis ranges from 0 to 12 in increments of 1. The y-axis ranges from 0 to 7 in increments of 1. The trend line starts at approximately left parenthesis 3 comma 3.8 right parenthesis and ends at approximately left parenthesis 11 comma 6.8 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis.
Image with alt text: Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend linearly upward. An upward trend line is plotted and labeled y equals 0.35 times x plus 2.8. The line follows the slope of the points. The x-axis ranges from 0 to 12 in increments of 1. The y-axis ranges from 0 to 7 in increments of 1. The trend line starts at approximately left parenthesis 3 comma 3.8 right parenthesis and ends at approximately left parenthesis 11 comma 6.8 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis.
2. Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend linearly upward. A horizontal line is plotted and labeled y equals 5. The line does not follow the slope of the points. The x-axis ranges from 0 to 12 in increments of 1. The y-axis ranges from 0 to 7 in increments of 1. The trend line starts at left parenthesis 3 comma 5 right parenthesis and ends at left parenthesis 11 comma 5 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis.
Image with alt text: Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend linearly upward. A horizontal line is plotted and labeled y equals 5. The line does not follow the slope of the points. The x-axis ranges from 0 to 12 in increments of 1. The y-axis ranges from 0 to 7 in increments of 1. The trend line starts at left parenthesis 3 comma 5 right parenthesis and ends at left parenthesis 11 comma 5 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis.
3. Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend linearly upward. A trend line is plotted and labeled y equals 0.35 times x plus 2.6. The line follows the slope of the points. "The x-axis ranges from 0 to 12 in increments of 1. The y-axis ranges from 0 to 7 in increments of 1. The trend line starts at approximately left parenthesis 3 comma 3.7 right parenthesis and ends at approximately left parenthesis 11 comma 6.4 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis.
Image with alt text: Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend linearly upward. A trend line is plotted and labeled y equals 0.35 times x plus 2.6. The line follows the slope of the points. "The x-axis ranges from 0 to 12 in increments of 1. The y-axis ranges from 0 to 7 in increments of 1. The trend line starts at approximately left parenthesis 3 comma 3.7 right parenthesis and ends at approximately left parenthesis 11 comma 6.4 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis.
4. Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend upward. A trend line is plotted that trends upward and is labeled y equals x minus 2. The line is at a different slope than the plotted points. The x-axis and y-axis ranges from 0 to 12 in increments of 1. The line starts at left parenthesis 3 comma 1 right parenthesis and ends at left parenthesis 11 comma 9 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis. The trend line intersects with the outer edge of the plotted point at left parenthesis 7 comma 4.8 right parenthesis.
Image with alt text: Quadrant 1 of a coordinate plane shows nine unlabeled plotted points that generally trend upward. A trend line is plotted that trends upward and is labeled y equals x minus 2. The line is at a different slope than the plotted points. The x-axis and y-axis ranges from 0 to 12 in increments of 1. The line starts at left parenthesis 3 comma 1 right parenthesis and ends at left parenthesis 11 comma 9 right parenthesis. The points are plotted at left parenthesis 3 comma 3.5 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 5 comma 4.2 right parenthesis, left parenthesis 6 comma 4.5 right parenthesis, left parenthesis 7 comma 4.8 right parenthesis, left parenthesis 8 comma 5.5 right parenthesis, left parenthesis 9 comma 5.8 right parenthesis, left parenthesis 10 comma 6.4 right parenthesis, and left parenthesis 11 comma 6.7 right parenthesis. The trend line intersects with the outer edge of the plotted point at left parenthesis 7 comma 4.8 right parenthesis.
The first option correctly uses a straight line to model the relationship between the variables in the table.
Use the image to answer the question.
Quadrant 1 of a coordinate plane has 3 plotted and labeled lines. Lines A and B decrease from left to right. Line C rises from left to right. 8 points are scattered on the plane. Points are plotted. Three lines are drawn on the plane. The x-axis ranges from 0 to 10 in one unit increments. The y-axis ranges from 0 to 10 in one unit increments. Line A is a downward sloping line that starts at left parenthesis 1 comma 7 right parenthesis and ends at left parenthesis 8 comma 0 right parenthesis. Line B is a downward sloping line that starts at left parenthesis 1 comma 6 right parenthesis and ends at left parenthesis 7 comma 0 right parenthesis. Line C is an upward sloping line that starts at left parenthesis 1 comma 1 right parenthesis and ends at left parenthesis 8 comma 8 right parenthesis. Lines A and B do not intersect and are parallel to each other. Lines B and C intersect at left parenthesis 3.5 comma 3.5 right parenthesis. Lines A and C intersect at left parenthesis 4 comma 4 right parenthesis. The points are plotted at coordinates left parenthesis 1 comma 0 right parenthesis, left parenthesis 2 comma 6.5 right parenthesis, left parenthesis 3 comma 4.5 right parenthesis, left parenthesis 4 comma 1 right parenthesis, left parenthesis 5 comma 3 right parenthesis, left parenthesis 6 comma 8 right parenthesis, left parenthesis 7 comma 4 right parenthesis, and left parenthesis 8 comma 2 right parenthesis.
Three trend lines were informally sketched on the graph. Which trend line best fits the data?
(1 point)
Responses
B
upper B
A
upper A
None of the lines fit the data, as the data have no association.
None of the lines fit the data, as the data have no association.
C
upper C
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The trend line that best fits the data is Trend Line C.
Use the image to answer the question.
An illustration of a scatterplot shows x on x-axis from 65 to 75 in increments of 1 and y on the y-axis from 200 to 240 in increments of 2.5. Eleven points are plotted. The approximate plotted points are as follows: left parenthesis 65 comma 205 right parenthesis, left parenthesis 67 comma 216 right parenthesis, left parenthesis 68 comma 210 right parenthesis, left parenthesis 68 comma 218 right parenthesis, left parenthesis 69 comma 224 right parenthesis, left parenthesis 70 comma 220 right parenthesis, left parenthesis 70 comma 224 right parenthesis, left parenthesis 71 comma 230 right parenthesis, left parenthesis 72 comma 235 right parenthesis, left parenthesis 74 comma 200 right parenthesis, and left parenthesis 74 comma 240 right parenthesis.
Is there a relationship between the two sets of data? How do you know?
(1 point)
Responses
No, because the data points are close to the trend line.
No, because the data points are close to the trend line.
Yes, because the data points are not close to the trend line.
Yes, because the data points are not close to the trend line.
No, because the data points are not close to the trend line.
No, because the data points are not close to the trend line.
Yes, because the data points are close to the trend line.
Yes, because the data points are close to the trend line.
No, because the data points are not close to the trend line.
Use the image to answer the question.
An illustration of a scatterplot shows x on x-axis from 65 to 75 in increments of 1 and y on the y-axis from 200 to 240 in increments of 2.5. Eleven points are plotted. The approximate plotted points are as follows: left parenthesis 65 comma 205 right parenthesis, left parenthesis 67 comma 216 right parenthesis, left parenthesis 68 comma 210 right parenthesis, left parenthesis 68 comma 218 right parenthesis, left parenthesis 69 comma 224 right parenthesis, left parenthesis 70 comma 220 right parenthesis, left parenthesis 70 comma 224 right parenthesis, left parenthesis 71 comma 230 right parenthesis, left parenthesis 72 comma 235 right parenthesis, left parenthesis 74 comma 200 right parenthesis, and left parenthesis 74 comma 240 right parenthesis.
Are there any outliers in the data shown on the scatterplot? If so, where?
(1 point)
Responses
Yes, at (74, 200)
Yes, at left parenthesis 74 comma 200 right parenthesis
Yes, at (65, 205)
Yes, at left parenthesis 65 comma 205 right parenthesis
No, there are no outliers in the data.
No, there are no outliers in the data.
Yes, at (74, 240)
Yes, at left parenthesis 74 comma 240 right parenthesis
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Yes, at (74, 200)
Use the image to answer the question.
An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 10 in increments of 1. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 8 comma 7 right parenthesis, and left parenthesis 10 comma 6.5 right parenthesis. 12 points are plotted close to the line.
Write an equation in slope-intercept form of the trend line.
(1 point)
Responses
y=−14x
y equals negative Start Fraction 1 over 4 End Fraction x
y=−58x+9
y equals negative Start Fraction 5 over 8 End Fraction x plus 9
y=−14x+9
y equals negative Start Fraction 1 over 4 End Fraction x plus 9
y=1x+9
y equals 1 x plus 9
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