Final answer:
To find the value of a, we set the slopes of the two lines equal to each other and solve for a. The value of a is 26.
Step-by-step explanation:
To determine the value of a, we can use the fact that parallel lines have the same slope. The slope of the line passing through the points (a, 1) and (-9, 8) can be found using the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the coordinates, we have: slope = (8 - 1) / (-9 - a). The slope of the line passing through the points (8, 5) and (a + 2, 1) can be found in a similar manner: slope = (1 - 5) / (a + 2 - 8). Since both lines are parallel, their slopes are equal, so we can set the two slope equations equal to each other and solve for a.
Start by setting the two slope equations equal to each other: (8 - 1) / (-9 - a) = (1 - 5) / (a + 2 - 8). Simplifying the equation: 7 / (-9 - a) = -4 / (a - 6). Now we can cross-multiply: 7(a - 6) = -4(-9 - a). Distributing and simplifying: 7a - 42 = 36 + 4a. Combine like terms: 3a = 78. Dividing by 3: a = 26.