Final answer:
The value of 'a' is determined to be 7 by first calculating the slope of the line that passes through the given points, then finding the line's equation, and finally substituting x = -2 into this equation to solve for 'a'.
Step-by-step explanation:
To find the value of a for the point (-2, a) that lies on line J, which also passes through the points (4,-2) and (6,-5), we need to determine the equation of the line and then use it to solve for a when x equals -2.
First, let's calculate the slope of the line (m) using the two given points:
m = (y2 - y1) / (x2 - x1)
m = (-5 - (-2)) / (6 - 4)
m = (-3) / 2
m = -1.5
Now that we have the slope, we can use point-slope form to find the equation of the line:
y - y1 = m(x - x1)
Let's use the point (4, -2) for this equation:
y - (-2) = -1.5(x - 4)
y + 2 = -1.5x + 6
y = -1.5x + 4
Finally, substitute x = -2 into the equation to find the y-coordinate:
a = -1.5(-2) + 4
a = 3 + 4
a = 7
Therefore, the value of a is 7.