Final answer:
The equation of the line passing through the points (4,9) and (8,2) is y = (-7/4)x + 16.
Step-by-step explanation:
The equation of the line that passes through the points (4,9) and (8,2) can be found using the slope-intercept form of a linear equation, which is y = mx + b. The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates of the points, we get m = (2 - 9) / (8 - 4) = -7/4.
Next, we can choose one of the points and substitute its coordinates into the equation to find the y-intercept (b). Using (4,9), we have 9 = (-7/4)(4) + b. Solving for b, we get b = 9 + 7 = 16. Therefore, the equation of the line is y = (-7/4)x + 16.