Final answer:
The slope-intercept form of the line passing through the points (4,1.9) and (5,2.1) is y = 0.2x + 1.1.
Step-by-step explanation:
The question asks for the equation of the line, in slope-intercept form, that contains the points (4,1.9) and (5,2.1). The slope-intercept form is represented as y = mx + b where m is the slope and b is the y-intercept. To find the equation of the line, first, we calculate the slope (m) by taking the difference in y-values divided by the difference in x-values between the two points:
m = (2.1 - 1.9) / (5 - 4) = 0.2 / 1 = 0.2
With the slope known, we then use one of the points to solve for b, the y-intercept, by substituting the values into the slope-intercept form.
Using the point (4,1.9):
1.9 = (0.2)(4) + b
b = 1.9 - 0.8
b = 1.1
Therefore, the equation of the line in slope-intercept form is:
y = 0.2x + 1.1