Every point on the line is a pair that works, and every pair that works is on the line.
Coordinates, briefly
The x value first, the y value second. The point (3, 2) is three along and two up, and the order matters.
Two points fix a line, but always plot a third. If one is out of line you know at once there is an error, and which value to recheck.
Drawing the graph of an equation
| Step | What to do |
|---|---|
| 1 | Choose three easy values of x, such as 0, 1 and 2 |
| 2 | Work out y for each and put them in a small table |
| 3 | Plot the three points, along first and then up |
| 4 | Check they are in a row, then join them with a ruled line |
Every point between them works too, including ones with fractions in. Three separate dots claim that only three pairs satisfy the equation.
Reading the equation from the line
In y = mx + c, the c is where the line crosses the vertical axis, and the m is how far it rises for every step to the right.
Read off the coordinates of any point on the line and put them into the equation. Both sides come out equal, every single time.
Unequal squares bend a straight line into something that is not straight. The numbers may all be correct while the picture tells a lie.
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