Trend Lines Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the question.
An illustration of a scatterplot shows x on x-axis from 70 to 84 in increments of 2 and y on the y-axis from 44 to 49 in increments of 0.5. Nine points are plotted and a line is drawn connecting a few of the dots along the path of a linear line. The x-axis ranges in increments of 2 and the y-axis ranges in increments of 0.5. The approximate plotted points are as follows: left parenthesis 70 comma 49 right parenthesis, left parenthesis 72 comma 48 right parenthesis, left parenthesis 73 comma 47.5 right parenthesis, left parenthesis 74 comma 47.5 right parenthesis, left parenthesis 76 comma 47 right parenthesis, left parenthesis 79 comma 46 right parenthesis, left parenthesis 80 comma 45.5 right parenthesis, left parenthesis 82 comma 45 right parenthesis, and left parenthesis 84 comma 44 right parenthesis. The line connects data points on the numbers on y-axis of 49, 47.5, 45.5, and 44 forming a negative slope.
Is the trend line on the scatterplot drawn correctly? Choose 1 for yes and 2 for no.
(1 point)
1. Yes
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 50 in increments of 10. 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 45 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 3 comma 15 right parenthesis, and left parenthesis 4.5 comma 0 right parenthesis. 13 points are plotted close to the line.
Write an equation in slope-intercept form of the trend line.
To find the equation of the trend line in slope-intercept form, we need to first calculate the slope using two points on the line. Let's choose the points (0, 45) and (4.5, 0).
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (0 - 45) / (4.5 - 0)
Slope (m) = -45 / 4.5
Slope (m) = -10
Now that we have the slope, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. We can choose any point on the line to find the y-intercept. Let's use the point (0, 45).
45 = -10(0) + b
45 = b
Therefore, the equation of the trend line in slope-intercept form is y = -10x + 45.
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 30 in increments of 2. Multiple points are plotted around a line that points upward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 6 comma 18 right parenthesis. 12 points are plotted close to the line.
Write an equation in slope-intercept form of the trend line.
To find the equation of the trend line in slope-intercept form, we need to first calculate the slope using two points on the line. Let's choose the points (0, 12) and (6, 18).
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (18 - 12) / (6 - 0)
Slope (m) = 6 / 6
Slope (m) = 1
Now that we have the slope, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. We can choose any point on the line to find the y-intercept. Let's use the point (0, 12).
12 = 1(0) + b
12 = b
Therefore, the equation of the trend line in slope-intercept form is y = x + 12.