Answer:
B
Step-by-step explanation:
To figure out equation of a line, we need two points.
If you look at the graph, one point is [tex](0,0)[/tex] and another point let's take [tex](1,1)[/tex].
The equation of the line is given by [tex]y=mx+b[/tex]
Where m is the slope with formula [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] and [tex](x_{1},y_{1})[/tex] is point 1 and [tex](x_{2},y_{2})[/tex] is point 2.
Solving for m, we have:
[tex]m=\frac{1-0}{1-0}\\m=\frac{1}{1}\\m=1[/tex]
Thus we have [tex]y=1x+c[/tex]
To solve for c [the y-intercept] we plug in any point into x and y of this equation. Let's use the point [tex](0,0)[/tex]. We have:
[tex]0=1(0)+c\\0=0+c\\c=0[/tex]
Thus we can write [tex]y=1x+0[/tex] or simply [tex]y=x[/tex]
In function notation, we replace [tex]y[/tex] with [tex]f(x)[/tex]
So we have [tex]f(x)=x[/tex]
Answer choice B is right.
