The equation of the line that best represents the trend of the given points is; y = -0.4x + 4.6
Finding the equation of a line that best represents the trend of the given points, using the slope-intercept form of a line, which is (y = mx + b).
Where: (m) is the slope
(b) is the y-intercept.
Calculate the slope (m) using two points from the given data, use (1,4.2) and (2,3.8):
m = change in y / change in x = (3.8 - 4.2) / (2 - 1) = -0.4
Find the y-intercept (b) using one of the points.
Using point (1,4.2):
4.2 = m × 1 + b
Substitute the calculated values of (m); and (b) into the slope-intercept form:
y = slope × x + y-intercept
This equation will represent a line that best fits the trend of the given points.
Calculate the values:
Solving for (b):
b = 4.6
Therefore, the equation of the line that best represents the trend of the given points is: y = -0.4x + 4.6