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
A y=1x+9
y equals 1 x plus 9
B y=−58x+9
y equals negative Start Fraction 5 over 8 End Fraction x plus 9
C y=−14x+9
y equals negative Start Fraction 1 over 4 End Fraction x plus 9
D y=−14x
The correct answer is C y=−14x+9. This equation represents the line that passes through the given points in the scatterplot.
To find the equation of the trend line in slope-intercept form, we need to determine the slope (m) and y-intercept (b).
Looking at the graph, we can see that the line points downward to the right, indicating a negative slope. The line passes through the points (0, 9), (4, 8), (8, 7), and (10, 6.5).
To calculate the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Let's choose the points (0, 9) and (8, 7) to calculate the slope.
m = (7 - 9) / (8 - 0)
= -2 / 8
= -1/4
Now we have the slope, let's find the y-intercept (b). We can select any point on the line, for convenience, let's choose (0, 9).
Using the slope-intercept form equation y = mx + b, we can substitute the known values:
9 = (-1/4)(0) + b
9 = b
So, the y-intercept (b) is 9.
Therefore, the equation of the trend line in slope-intercept form is:
y = -1/4x + 9.
Therefore, the correct answer is:
C) y = -(1/4)x + 9
To write an equation in slope-intercept form of the trend line, we need to determine the slope and y-intercept of the line.
From the given information, we can observe that the line passes through the points (0, 9), (4, 8), (8, 7), and (10, 6.5). We can use these points to calculate the slope of the line.
The slope of a line can be calculated using the formula:
slope = (change in y) / (change in x)
Using the points (0, 9) and (10, 6.5):
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:
y - y1 = m(x - x1)
Using any of the given points, let's take (0, 9):
y - 9 = -0.25(x - 0)
y - 9 = -0.25x
To convert the equation into slope-intercept form (y = mx + b), we can rearrange the equation to isolate y:
y = -0.25x + 9
Therefore, the equation in slope-intercept form of the trend line is:
y = -0.25x + 9
So, the correct answer is C.