Two lines are parallel if their slopes are equal. To find the slope of the line through the points (1,2) and (1,a), we can use the formula:
(y2 - y1) / (x2 - x1) = (a - 2) / (1 - 1) = a - 2
To find the slope of the line 6x + 2y = -2, we can rewrite it in slope-intercept form (y = mx + b) by isolating y:
2y = -6x - 2
y = -3x - 1
So the slope of this line is -3.
Since the line through the points (1,2) and (1,a) is parallel to 6x + 2y = -2, we know that the slopes must be equal. Therefore:
a - 2 = -3
Solving for a:
a = -1
So the value of a is -1.