Final answer:
The equation of the line passing through the points (8,1) and (4,4) is y = -3/4x + 7.
Step-by-step explanation:
To find the equation of a line that passes through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m):
m = (y2 - y1) / (x2 - x1) = (4 - 1) / (4 - 8) = 3 / -4 = -3/4
Next, we can choose either point (8,1) or (4,4) to substitute into the equation and find the y-intercept (b). Let's use (8,1):
1 = (-3/4)(8) + b
b = 1 + (3/4)(8) = 1 + 6 = 7
Therefore, the equation of the line that passes through the points (8,1) and (4,4) is y = -3/4x + 7.