# What are examples of using graphs to help solve word problems?

##### 1 Answer

Here is a simple example of a word problem where graph helps.

From a point

Later on, at time

At what time the second car catches on with the first, that is both will be on the same distance from point

*Solution*

It makes sense to define a function that represents a dependency of the distance

The first car started at

The second car started later by

Algebraically, the solution to this problem can be found by solving an equation

that results in

Obviously,

Let's use concrete numbers:

Then the solution is:

If we are not so well versed in Algebra and equations to construct the equation above, we can use graphs of these two functions to visualize the problem.

The graph of a function

graph{x [-1, 10, -1, 10]}

The graph of a function

graph{1.5x+|1.5x-3|-3 [-1, 10, -1, 10]}

If we draw both graphs on the same coordinate plane, the point they intersect (looks like

In this and many other cases the graph might not provide an exact solution, but it helps a lot to understand the reality behind a problem.

Moreover, graphical representation of a problem would help to find a precise analytical approach to exact solution. In the example above this process of intersecting two graphs gives a strong hint to an equation used to algebraically solve the problem.