Final answer:
To determine the value of a for the slope to equal 6 between the points (3,2) and (4,a), the slope formula is applied, which yields a value of a = 8.
Step-by-step explanation:
To find the value of a so that the slope of the line passing through the points (3,2) and (4,a) is 6, we can use the slope formula, which is (y2 - y1) / (x2 - x1). In this case, we have the following:
Slope (m) = (a - 2) / (4 - 3)
Since we are given that the slope (m) equals 6, we can set up the equation:
6 = (a - 2) / 1
To find the value of a, we multiply both sides of the equation by 1 and then add 2 to both sides, resulting in:
6 = a - 2
a = 6 + 2
= 8
Therefore, the value of a is 8 for the slope to be 6.