How do I explain Euler method? The explicit Euler method for numerically solving the begining values of differential equation $x′=f(t,x),x(t_0)=x_0$ on the interval $I = [t_0, T]$ is given by 
$x_{k+1}=x_k+hf(t_k,x_k),k=0,…,N−1$  with $h = (T - t_0) / N, N ∈ N. $
$X_k$ is an approximation of the exact solution $x(t)$ of the begining values at time $t_k: = t_0 + kh, k = 0, ..., N.$ By linear interpolation between the points $(t_k, x_k)$ and $(t_{k + 1}, x_{k + 1}), k = 0, ..., N -1,$ we obtain a approximation solution $x_h(t)$.
Can someone tell if this sketch is good?



The graph looks good. You could think about including a second step to emphasize, that the approximation error accumulates from step to step. But the main point of using the slope at $ x_k $ to approximate $ x_{k+1} $ is clear form the graph.
Cheers
