3 Steps, because you do not know the cut off point.
Step 1: Set the cut off point at $x_0$. Create a dummy variable $Z = 1$ if $x>x_o$, = 0 otherwise. Fit a model
$$ y = \beta_0 + \beta_1x+\beta_2Z+\beta_3Zx+\epsilon$$
Then $\beta_1$ is the slope for $x \le x_0$ and $\beta_1 + \beta_3$ is the slope for $x > x_0$. Record SSE (Sum of square of error) and $x_0$.
Step 2: Pick-up the different $x_0$ to repeat Step 1. After 3 times, create scatter plot with $x_0$ as x axis and SSE as y axis. From this graph, you will be able to find what is next $x_0$ so that the SSE will decrease. Repeat until you think you find $x_0$ such that SSE reach the lowest value. It is selected model.
Step 3: Fit a model $$ y = \beta_0 + \beta_1x + \epsilon$$
Using difference of SSE to construct an F test to compare if the data following the two pieces of linear model. Here need to pay attention to DF (degree of freedom). Although 4 and 2 regression coefficients are estimated in selected model and the last model, but in fact the cut off point is also estimated, so the DF for difference of SSE should be 3, instead of 2.