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?
A. No, because the data points are not close to the trend line.
B. Yes, because the data points are not close to the trend line.
C. No, because the data points are close to the trend line.
D. Yes, because the data points are close to the trend line.
D. Yes, because the data points are close to the trend line.
The fact that the data points are close to the trend line indicates that there is a relationship between the two sets of data. This suggests that as x increases, y also tends to increase.
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?
A. No, there are no outliers in the data.
B. Yes, at (74, 200)
C. Yes, at (65, 205)
D. Yes, at (74, 240)
D. Yes, at (74, 240)
The point (74, 240) appears to be an outlier as it is significantly different from the pattern observed in the rest of the data. The majority of the other points cluster around a general trend, but this point is much further away from that pattern.
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.
A. y = −14x + 9
B. y = −58x + 9
C. y = −14x
D. y= 1x + 9
The correct answer is
A. y = -0.5x + 9
To find the slope of the trend line, you need to calculate the change in y divided by the change in x.
Slope (m) = (change in y) / (change in x)
From the given points:
(0, 9) and (4, 8): (8 - 9) / (4 - 0) = -1 / 4 = -0.25
(4, 8) and (8, 7): (7 - 8) / (8 - 4) = -1 / 4 = -0.25
(8, 7) and (10, 6.5): (6.5 - 7) / (10 - 8) = -0.5 / 2 = -0.25
Since all the calculations give the same slope of -0.25, you can use any pair of points to find the equation of the trend line. Let's use the point (0, 9).
y = mx + b, where m is the slope and b is the y-intercept.
Substituting the slope and point (0, 9) into the equation gives:
9 = -0.25(0) + b
b = 9
Therefore, the equation of the trend line is:
y = -0.25x + 9
Simplifying, you get:
y = -0.5x + 9
That doesn't match the answers
I apologize for the oversight. Let's correct the calculation.
From the given points:
(0, 9) and (4, 8): (8 - 9) / (4 - 0) = -1 / 4 = -0.25
(4, 8) and (8, 7): (7 - 8) / (8 - 4) = -1 / 4 = -0.25
(8, 7) and (10, 6.5): (6.5 - 7) / (10 - 8) = -0.5 / 2 = -0.25
The slope is consistently -0.25.
Using point (0, 9) to find the equation of the trend line:
y = mx + b
9 = -0.25(0) + b
b = 9
Therefore, the equation of the trend line is:
y = -0.25x + 9
The correct answer should be:
A. y = -0.25x + 9
Use the image to answer the question.
A scatterplot graph shows x-axis ranging from 0 to 100 and y-axis ranging from 0 to 50. Both axes are drawn in increments of 5 but labeled in increments of 10. Multiple points are plotted around a line that points upward to the right.
The line passes through left parenthesis 0 comma 30 right parenthesis, left parenthesis 15 comma 40 right parenthesis, and left parenthesis 30 comma 50 right parenthesis. 14 points are plotted close to or on the line. The line has an arrowhead on the top of it.
Write an equation in slope-intercept form of the trend line.
A. y = 23x + 30
B. y = 34x + 30
C. y = −23x + 30
D. y = 23x + 40
To find the equation of the trend line, we first need to determine the slope of the line. The slope (m) is given by the change in y divided by the change in x.
From the given points:
(0, 30) and (15, 40): (40 - 30) / (15 - 0) = 10 / 15 = 2/3
(15, 40) and (30, 50): (50 - 40) / (30 - 15) = 10 / 15 = 2/3
The slope is consistent at 2/3.
Now we can use any of the points, let's use point (0, 30), and the slope to find the y-intercept (b).
y = mx + b
30 = (2/3)(0) + b
b = 30
Therefore, the equation of the trend line is:
y = (2/3)x + 30
However, to match the format of the answer choices, we can simplify the equation to slope-intercept form:
y = 2/3 x + 30
The correct answer choice corresponding to this format is not among the ones provided. So, "y = 23x + 30" is not a valid option, but the correct equation is y = (2/3)x + 30, better represented as:
y = 2x/3 + 30
Use the image to answer the question.
A scatterplot graph shows x-axis ranging from 0 to 100 and y-axis ranging from 0 to 50. Both axes are drawn in increments of 5 but labeled in increments of 10. Multiple points are plotted around a line that points upward to the right.
The line passes through left parenthesis 0 comma 30 right parenthesis, left parenthesis 15 comma 40 right parenthesis, and left parenthesis 30 comma 50 right parenthesis. 14 points are plotted close to or on the line. The line has an arrowhead on the top of it.
Write an equation in slope-intercept form of the trend line.
A. y = 2/3x + 30
B. y = 3/4x + 30
C. y = −2/3x + 30
D. y = 2/3x + 40