The line passes through (3, a), (2, 4) and (b, 4). The line passes through (2, 4) and (b, 4). This is the case when the line is horizontal and the equation of the line is y = 4
As it passes through (3, a), a = 4
y = 4 is true for any value of b where b is the x-coordinate of a point (b, 4)
The required value of a = 4 and b can take on any value.
It is given that a line passes through the points (3, a), (2, 4) and (b, 4).
The slope of a line passing through the points (x1, y1) and (x2, y2) is:
`m = (y2 - y1)/(x2 - x1)`
Substituting the co-ordinates of the points that the line passes through, the slope of the line is given by:
`m = (4 - a)/(2 - 3) = (4 - a)/(-1)` and by `m = (4 - 4)/(b - 2) = 0`
Equating the values of m obtained, `(4 - a)/(-1) = 0` gives:
4 - a = 0
a = 4
Also, `(4 - 4)/(b - 2) = 0` for all values of b
Therefore, from the data provided a unique value of only the variable a can be determined and that is a = 4.