To find an equation of the line passing through the given points (1,1) and (2,6), we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is one of the given points.
To find the slope, we can use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (1,1) and (x2, y2) = (2,6).
Substituting these values, we get:
m = (6 - 1)/(2 - 1) = 5
Therefore, the equation of the line passing through the given points is:
y - 1 = 5(x - 1)
Using function notation, we can write this equation as:
f(x) = 5x - 4