Interpret points on a graph in context

Detailed Explanation: Interpret points on a graph in context

A point on a graph gives two connected pieces of information:

• The horizontal coordinate tells the input.
• The vertical coordinate tells the output.

Always check the axis labels, scales, and units before explaining a point. Then write the ordered pair as $(x,y)$, where $x$ comes first.

Example

A graph shows the amount of water in a tank over time.

• The horizontal axis is time in minutes.
• The vertical axis is water in liters.
• The graph has a point $P$ at $(3,8)$.

Step 1: Read the horizontal coordinate

The first number is $3$. Because the horizontal axis shows time, the input is 3 minutes.

Step 2: Read the vertical coordinate

The second number is $8$. Because the vertical axis shows water, the output is 8 liters.

Step 3: Explain the point in words

The point $(3,8)$ means:

After 3 minutes, the tank contains 8 liters of water.

The order matters. It would not mean 8 minutes and 3 liters.

Step 4: Interpret other points on the line

Every point on the line represents a time and the amount of water in the tank at that time. For example, if the line passes through $(2,6)$, then:

After 2 minutes, the tank contains 6 liters of water.

If you look at the line halfway between 2 and 3 minutes, you might estimate the amount of water to be about 7 liters. You could describe this as:

After about 2.5 minutes, the tank contains about 7 liters of water.

Use words such as about or approximately when you are reading a location between marked grid points. A point placed exactly on a grid intersection gives an exact value, such as $(3,8)$.