5What is an intersection point? (2/2)

Since points in the coordinate system are always expressed by $\sf x$ and $\sf y$, the axis "time" is set as $\sf x$-axis and "distance travelled" as $\sf y$-axis.

The straight line equations from the story now look like this:

• Tortoise: $\sf y = \frac{1}{2}x + 3$

• Hare: $\sf y = \frac{3}{4}x$

So the point where two straight lines cross is the meeting point mentioned above. This is called an intersection point in mathematics. By reading off the intersection point from the graph, you can find the solution to the problem.

Check the intersection point

Once you have read an intersection point from the graph, you can substitute it into your two straight line equations to check it. The coordinates of the intersection are $\sf P\;(\color{#CC0000}{12}|\color{#009999}{9})$.

Tortoise: $\sf y = \frac{1}{2}x + 3$

Hare: $\displaystyle \sf y = \frac{3}{4}x$

Insert the coordinates of the intersection.

Tortoise: $\displaystyle \sf \color{#009999}{9}=\frac{1}{2}\cdot \color{#cc0000}{12} +39=21⋅12+3$

Hare: $\displaystyle \sf \color{#009999}{9}=\frac{3}{4}\cdot \color{#cc0000}{12}$

If you get two true statements, you have read off the correct intersection.

Tortoise: $\sf \color{#009999}{9}=9$

Hare: $\displaystyle \sf \color{#009999}{9}=9$

Since both statements are true, you know that you have determined the intersection correctly.