Trend Lines Quick Check
1 of 51 of 5 Items
Question
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
Yes, because the data points are not close to the trend line.
Yes, 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.
No, because the data points are not close to the trend line.
No, because the data points are close to the trend line.
No, because the data points are not close to the trend line. Trend lines show the general direction of the data and how one variable affects the other. If the data points are not close to the trend line, it indicates that there is not a strong relationship between the two sets of data.
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.
To write the equation of the trend line in slope-intercept form, we first need to find the slope of the line. We can choose two points on the line, such as (0, 9) and (10, 6.5), to calculate the slope.
Slope (m) = (y2 - y1) / (x2 - x1)
Slope = (6.5 - 9) / (10 - 0)
Slope = -2.5 / 10
Slope = -0.25
Now that we have the slope, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using point (0, 9) as the point on the line, we get:
y - 9 = -0.25(x - 0)
y - 9 = -0.25x
To convert this to slope-intercept form (y = mx + b), we can move 9 to the right side of the equation:
y = -0.25x + 9
Therefore, the equation of the trend line in slope-intercept form is 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.
(1 point)
Responses
y=23x+30
y equals Start Fraction 2 over 3 End Fraction x plus 30
y=−23x+30
y equals negative Start Fraction 2 over 3 End Fraction x plus 30
y=34x+30
y equals Start Fraction 3 over 4 End Fraction x plus 30
y=23x+40
To write the equation of the trend line in slope-intercept form, we first need to find the slope of the line. We can choose two points on the line, such as (0, 30) and (30, 50), to calculate the slope.
Slope (m) = (y2 - y1) / (x2 - x1)
Slope = (50 - 30) / (30 - 0)
Slope = 20 / 30
Slope = 2/3
Now that we have the slope, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using point (0, 30) as the point on the line, we get:
y - 30 = 2/3(x - 0)
y - 30 = 2/3x
To convert this to slope-intercept form (y = mx + b), we can move 30 to the right side of the equation:
y = 2/3x + 30
Therefore, the equation of the trend line in slope-intercept form is y = (2/3)x + 30, which is equivalent to y = 23x + 30. The correct response is y = 23x + 30.
Use the image to answer the question.
A scatterplot graph shows x-axis ranging from 0 to 50 and y-axis ranging from 0 to 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The x-axis is drawn in increments of 5 but labeled in increments of 10. The y-axis is drawn in increments of 1 but labeled in increments of 2. The line passes approximately through left parenthesis 0 comma 8 right parenthesis, left parenthesis 10 comma 6 right parenthesis, left parenthesis 15 comma 5 right parenthesis, left parenthesis 20 comma 4 right parenthesis, left parenthesis 25 comma three right parenthesis, and left parenthesis 40 comma 0 right parenthesis. 14 points are plotted close to or on the line.
Write an equation in slope-intercept form of the trend line.
(1 point)
Responses
y=−15x+8
y equals negative Start Fraction 1 over 5 End Fraction x plus 8
y=15x+8
y equals Start Fraction 1 over 5 End Fraction x plus 8
y=−15x+3
y equals negative Start Fraction 1 over 5 End Fraction x plus 3
y=5.67x+8
y equals 5.67 x plus 8
To write the equation of the trend line in slope-intercept form, we first need to find the slope of the line. We can choose two points on the line, such as (0,8) and (15,5), to calculate the slope.
Slope (m) = (y2 - y1) / (x2 - x1)
Slope = (5 - 8) / (15 - 0)
Slope = -3 / 15
Slope = -1/5
Now that we have the slope, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using point (0,8) as the point on the line, we get:
y - 8 = -1/5(x - 0)
y - 8 = -1/5x
To convert this to slope-intercept form (y = mx + b), we can move 8 to the right side of the equation:
y = -1/5x + 8
Therefore, the equation of the trend line in slope-intercept form is y = -1/5x + 8, which is equivalent to y = -0.2x + 8. The correct response is y = -0.2x + 8.