Kid-friendly explanation
Imagine a big map made of squares, like graph paper. The y-axis is the straight line that goes up and down through the middle. Numbers above the middle are positive, and numbers below the middle are negative. The y-axis tells how high or low a point is.
Worked examples
Example 1 (upper elementary): locating a point on the y-axis
On a coordinate plane, look at the point with coordinates (0, 4).
The first number, 0, is the x-coordinate, which tells how far left or right the point is. Since it is 0, the point is not left or right of the origin. The second number, 4, is the y-coordinate, which tells how far up or down the point is. Since it is 4, the point is 4 units above the origin, on the y-axis.
Example 2 (middle/high school): reflection across the y-axis
Consider the point A at (3, -2). Reflect A across the y-axis to get point A'.
Reflecting across the y-axis means you move the point to the opposite side of the y-axis, the same distance away. The x-coordinate changes sign, and the y-coordinate stays the same. So (3, -2) becomes (-3, -2). Point A' is at (-3, -2), which is the reflection of A across the y-axis.
Going deeper with the y-axis
The y-axis is one of the two main axes on the coordinate plane. Together with the x-axis, it divides the plane into four quadrants and helps name the location of any point using an ordered pair (x, y).
In transformations, such as reflections, the y-axis is used as a mirror line. Reflecting a point (a, b) across the y-axis gives the point (-a, b). Whole figures can be reflected this way, and the new figure is congruent, meaning it has the same size and shape as the original.
In more advanced graphing, the y-axis is where you read the vertical values of a graph. For example, in a line written in slope-intercept form, y = mx + b, the line crosses the y-axis at the y-intercept (0, b).
Common mistakes with the y-axis
- Mixing up the x-axis and y-axis. A common mistake is thinking the y-axis goes left and right. The correction is that the y-axis is always the vertical (up and down) axis, and the x-axis is the horizontal (left and right) axis.
- Switching x and y in ordered pairs. A student might plot (2, 5) by going 5 units right and 2 units up, landing at (5, 2) instead. The correction is to remember that the first number is the x-coordinate (left/right) and the second number is the y-coordinate (up/down).
- Reflecting across the wrong axis. When asked to reflect a point across the y-axis, a student might change the y-coordinate instead, turning (3, -2) into (3, 2). The correction is that reflection across the y-axis changes the sign of the x-coordinate only, so (3, -2) becomes (-3, -2).
Where the y-axis shows up in everyday life
The idea of the y-axis appears in many everyday graphs and charts. On a bar graph of weekly allowance, the y-axis might show how many dollars are saved, while the bottom line shows the days of the week. On a line graph of temperature, the y-axis shows how hot or cold it is as time changes.