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

A similar question can be found at

point a is the center of this circle.

the ratio of the lengths of (ef/bc) and (ad/ih) is 2: 1.

step-by-step explanation:

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers