Derek walks to his best friends house at a rate of 1 block per minute, then turns around and walks home. The graph shows the distance Derek walks in the given amount of time. Write an equation for the graph.

In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:

Equation of a line:

The equation of a line is given by:

In which m is the slope and b is the y-intercept(value of y when x = 0).

This situation:

x between 0 and 10:

From here, we can take two points (t,y). I will take (0,0) and (10,10).

From point (0,0), we get that when , which means that the y-intercept is , thus:

To find the slope, when we have two points, it is given by change in y divided by change in t, so:

Change in t: 10 - 0 = 10

Change in y: 10 - 0 = 10

Slope:

Thus, the first definition is:

x between 10 and 20:

I will take the points (10,10) and (20,0).

First, we find the slope:

Change in t: 20 - 10 = 10

Change in y: 0 - 10 = -10

Slope:

Thus:

For the intercept, we have point (20,0), which means that when . So

Thus, the second definition is:

Write an equation for the graph.

We use the two definitions, that is:

So

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