Graphing calculator example
Make a table of values from an equation
A table turns an equation into a few specific points. Start with y = 2x + 1: choose an x value, substitute it, and calculate y. Then place each pair on the graph.
Try it on the graph
y = ax + 1
Solid: current graph. Dashed: starting graph. Axes use the labeled scales.
| x | y |
|---|---|
| -3 | |
| -1 | |
| 1 | |
| 3 | |
| 5 |
Values are rounded to seven significant digits.
Work one row: x = 2
- Replace x with 2 in y = 2x + 1.
- Multiply first: 2 × 2 = 4. Then add 1, giving y = 5.
- The row is (2, 5). Its point lies two units right of the origin and five units up.
What to notice
With a = 2, increasing x by 1 increases y by 2. That constant change produces a straight line.
Changing a changes the slope, but x = 0 always gives y = 1 in this example.
A table shows selected inputs, not every point on a graph. For other functions, some inputs can be undefined: 1/x has no value at x = 0.
Check your understanding
Set a = −1. Before selecting a row, predict the value at x = 2. Check that the result is −1.
Keep exploring
The full calculator lets you edit equations, add more curves, set axis bounds, and share or export your graph. The examples here use ordinary real-number arithmetic; graph lines and computed values are numerical approximations.
Open the graphing calculator →