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.