Final answer:
To find the value of 'a', we establish that parallel lines have the same slope. The slope of the given line is 1, and using the slope formula, we determine that 'a' must be 3 for the lines to be parallel.
Step-by-step explanation:
To find the value of a for a line that is parallel to another, we must first understand that parallel lines have the same slope. The equation given for the line that we want to be parallel to is y = (x + 2). This can be rewritten to fit the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope m is 1 because the equation is simply y = 1x + 2.
The line passing through the points (a, -5) and (2,-6) must have the same slope of 1 to be parallel to the original line. To find the slope of the line through these two points, we use the slope formula m = (y2 - y1) / (x2 - x1). Thus, we have:
m = (-6 - (-5)) / (2 - a)
m = (-1) / (2 - a)
Since the slopes must be equal for the lines to be parallel, we set the slopes equal to each other:
1 = (-1) / (2 - a)
Multiplying both sides by (2 - a) gives us:
2 - a = -1
Adding a to both sides and adding 1 to both sides we get:
a = 2 + 1
a = 3
Therefore, for the line through the points (a, -5) and (2, -6) to be parallel to the line represented by y = (x + 2), the value of a must be 3.