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+3
y equals negative Start Fraction 1 over 5 End Fraction x plus 3
y=15x+8
y equals Start Fraction 1 over 5 End Fraction x plus 8
y=5.67x+8
y equals 5.67 x plus 8
Skip to navigation
The correct answer is:
y=-0.3x+8
To find the equation of the trend line in slope-intercept form, we need to determine the slope and the y-intercept.
From the scatterplot graph, we can observe that the line passes through the points (0, 8) and (40, 0).
The slope of a line can be calculated using the formula:
slope = (change in y) / (change in x)
Substituting the values, we get:
slope = (0 - 8) / (40 - 0) = -8 / 40 = -1/5
Now, let's use the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept.
We can substitute the calculated slope (-1/5) and the coordinates of one of the points (0, 8) into the equation and solve for b:
8 = (-1/5)(0) + b
8 = b
Therefore, the y-intercept (b) is 8.
Therefore, the equation of the trend line in slope-intercept form is:
y = -1/5x + 8
Therefore, the correct answer is: y equals negative Start Fraction 1 over 5 End Fraction x plus 8.
To find the equation of the trend line in slope-intercept form, we need to determine the slope and the y-intercept of the line.
From the information given in the description:
- The line passes approximately through the points (0, 8), (10, 6), (15, 5), (20, 4), (25, 3), and (40, 0).
- The line points downward to the right.
To find the slope, we can choose any two points on the line and use the slope formula:
slope (m) = (change in y)/(change in x)
Let's choose the points (0, 8) and (25, 3):
slope = (3 - 8)/(25 - 0) = -5/25 = -1/5
Now that we have the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Using the point (0, 8) and the slope of -1/5:
y - 8 = -1/5(x - 0)
y - 8 = -1/5x
y = -1/5x + 8
Therefore, the equation of the trend line in slope-intercept form is y = -1/5x + 8.
So, the correct answer is:
y = -1/5x + 8.