Final answer:
The equation of the line that passes through the points (4,4) and (8,1) is y = -3/4x + 7, which is not represented by any of the given options. The student should recheck the options provided.
Step-by-step explanation:
To find the equation of the line that passes through the points (4,4) and (8,1), we first calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into this formula, we get:
m = (1 - 4) / (8 - 4) = -3/4
With the slope calculated, we use one of the points to find the y-intercept (b). Using the point-slope form y - y1 = m(x - x1), we have:
y - 4 = (-3/4)(x - 4)
Expanding and simplifying:
y = (-3/4)x + 3 + 4
y = (-3/4)x + 7
Therefore, the fully reduced form of the equation for the line is y = -3/4x + 7, which does not match any of the provided options. The student may need to double check the options, as none of them correspond to the correct equation derived from the given points.