Here’s a really neat way you can use your TI-83 or TI-84 graphing calculator to find the equation of a line passing through two points, as well as its slope and y-intercept.
In this example, let’s figure out the equation of a line passing through (2,-3) and (4, 1).
1.) Press STAT, and select Edit by pressing ENTER.
2.) Enter in the x-coordinates into L1, and the y-coordinates into L2. For example, to enter in the point (2, -3), put 2 into the first row of L1, and -3 into the first row of L2. To enter in the point (4, 1), put 4 into second row of L1, 1 into the second row of L2.
3.) Press STAT again, and this time hit the right arrow over to select the Calc menu.4.) Select option 4, LinReg (short for linear regression). Press ENTER.5.) You will see a window that says y = ax + b on your TI-83 or TI-84 graphing calculator.
Here, a is the slope, and b is the y-intercept.
In this case, the slope is 2, the y-intercept is -7, and equation of the line is y = 2x – 7.