Determine the linear function that passes through the points (2,1) and (1,1).
You may use the slope point form of equation of the line, such that:
`f(x) - f(x_0) = m(x - x_0)`
Considering `(x_0,y_0) = (1,1)` yields:
`f(x) - 1 = m(x - 1)`
You need to evaluate the slope m, using slope equation, such that:
`m = (y - y_0)/(x - x_0)`
`m = (1 - 1)/(2 - 1)=> m = 0`
`f(x) - 1 = 0(x - 1) => f(x) = 1`
Since the slope m = 0, hence, the line passing through the given points,` f(x) = 1` , is parallel to x axis.
We'll write the form of a linear function:
f(x) = ax + b
A linear function is determined when it's coefficients are determined. So, we'll have to determine the coefficients a and b.
Since the function is determined by the points (2,1) and (1,1), that means that if we'll substitute the coordinates of the points into the expression of the function, we'll get the relations:
f(2) = 1
f(2) = a*2 + b
2a + b = 1 (1)
f(1) = 1
f(1) = a+b
a + b = 1 (2)
We'll put (1) = (2):
2a + b = a + b
We'll combine and eliminate like terms:
2a - a = b - b
a = 0
We'll substitute a in (2):
b = 1
Since the expression of the function is: f(x) = 1, the function is not linear, but constant.