Answer:
a = -1
Explanation:
Since the new line is parallel to line m, it has the same slope as line m. We can find the slope of line m by looking at its equation:
2x + 4y = 8
Subtracting 2x from both sides, we get:
4y = -2x + 8
Dividing both sides by 4, we get:
y = -1/2x + 2
Therefore, the slope of line m is -1/2.
We also know that the new line passes through the point (-6,2). We can use this point and the slope of the line to find the value of a in the equation y = 1/2x + a.
Starting with the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the values we know:
y - 2 = -1/2(x - (-6))
y - 2 = -1/2(x + 6)
y - 2 = -1/2x - 3
Adding 3 to both sides, we get:
y + 1 = -1/2x
Subtracting 1 from both sides, we get:
y = -1/2x - 1
Comparing this equation to y = 1/2x + a, we see that a = -1.
Therefore, the value of a in the equation y = 1/2x + a for the new line that passes through the point (-6,2) and is parallel to line m is a = -1.