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.
(1 point)
y=
Using the coordinates given, we can calculate the slope of the line.
Slope (m) = (y2 - y1)/(x2 - x1) = (0 - 45)/(4.5 - 0) = -10
Now we can use the point-slope form of the equation of a line to find the equation of the trend line, using any point on the line (such as (0, 45)).
y - y1 = m(x - x1)
y - 45 = -10(x - 0)
y - 45 = -10x
y = -10x + 45
Therefore, the equation in slope-intercept form of the trend line is:
y = -10x + 45
To find the equation of the trend line in slope-intercept form, we need to determine the slope and y-intercept.
From the given information, we can see that the line passes through two points:
Point 1: (0, 45)
Point 2: (4.5, 0)
Using the formula for slope:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates into the formula:
m = (0 - 45) / (4.5 - 0)
m = -45 / 4.5
m = -10
Now that we have the slope, we can use it to find the y-intercept. We choose one of the points, let's use (0, 45), and substitute the values into the slope-intercept form equation (y = mx + b), solving for b:
45 = -10(0) + b
45 = b
Therefore, the equation of the trend line in slope-intercept form is:
y = -10x + 45
To determine the equation of the trend line in slope-intercept form, we need to know the slope and y-intercept of the line.
From the given information, we can observe that the line passes through four points: (0, 45), (2, 25), (3, 15), and (4.5, 0).
To find the slope of the line, we can use the formula:
slope = (change in y) / (change in x)
Using the points (0, 45) and (4.5, 0), we can calculate the slope:
slope = (0 - 45) / (4.5 - 0) = -45 / 4.5 = -10
Now that we have the slope of the line, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (0, 45) and the slope we found (m = -10):
y - 45 = -10(x - 0)
y - 45 = -10x
To convert it to the slope-intercept form (y = mx + b), we can rearrange the equation:
y = -10x + 45
Therefore, the equation of the trend line in slope-intercept form is:
y = -10x + 45.