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