Slope measures how steep a line is: how much it rises (or falls) for every one unit you move to the right. It is often remembered as “rise over run”. A slope of 2 means the line goes up 2 units for each 1 unit across.
Once you have the slope, the y-intercept b tells you where the line crosses the y-axis. Plug either point into y = mx + b and solve for b. Together, m and b give the slope-intercept form of the line.
The distance between the points comes from the Pythagorean theorem, treating the run and rise as the two legs of a right triangle. The angle of inclination is the angle the line makes with the positive x-axis.
Frequently asked questions
What does an undefined slope mean?
If both points have the same x-coordinate, the run is zero and you would be dividing by zero. The line is vertical and its equation is x = constant.
Does the order of the points matter?
No. Swapping the points flips the sign of both the rise and the run, so their ratio — the slope — stays the same.
How do I write the point-slope form?
Use y − y₁ = m(x − x₁). With m = 2 and the point (1, 2), that is y − 2 = 2(x − 1), which simplifies to y = 2x.