Answer:
The linear function is
[tex]f(x)=x-5[/tex]
Step-by-step explanation:
Given values:
[tex]f(10)=5[/tex]
[tex]f(2)=-3[/tex]
From the given values, we can identify the points on the line.
For [tex]f(x)=y[/tex] point can be given as [tex](x,y)[/tex]
So, the points are:
[tex](10,5)[/tex] and [tex](2,-3)[/tex]
Using the points we can find slope of the line [tex]m[/tex].
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-3-5}{2-10}[/tex]
[tex]m=\frac{-8}{-8}[/tex]
∴ [tex]m=1[/tex]
Using point slope equation to find equation of line.
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] is a point on line.
Using point (10,5) and slope [tex]m=1[/tex] to find equation of line.
[tex]y-5=1(x-10)[/tex]
Simplifying.
[tex]y-5=x-10[/tex]
Adding 5 both sides.
[tex]y-5+5=x-10+5[/tex]
[tex]y=x-5[/tex]
So, the function can be written as:
[tex]f(x)=x-5[/tex] [ ∵ [tex]y=f(x)[/tex] ]
