Enter a value for slope (m) and y-intercept (b) in the fields on the left. The graph updates live as you type. You will see the line drawn on the coordinate grid with the slope and intercept labelled. Try changing m to see how the steepness shifts, then adjust b to move the line up or down.
The equation y = mx + b is called slope-intercept form. It is the most useful way to write a linear equation because it tells you two things instantly: the slope (m) and where the line crosses the y-axis (b).
The slope m tells you how the y value changes for every 1 unit increase in x. If m = 3, then y goes up by 3 every time x goes up by 1. If m is negative, the line goes downward as x increases. The y-intercept b is the starting point. When x = 0, y equals b.
| Slope (m) | What the Line Looks Like |
|---|---|
| m = 3 | Steep upward line, rises quickly |
| m = 0.5 | Gentle upward line, gradual rise |
| m = 0 | Perfectly horizontal line |
| m = -1 | Diagonal downward line at 45 degrees |
| m = -3 | Steep downward line, drops quickly |
Pick any two points on the line. Slope = rise divided by run. Rise is how much y changes between the two points. Run is how much x changes. If you go from (1, 2) to (3, 8), the rise is 8 - 2 = 6 and the run is 3 - 1 = 2. So slope = 6 / 2 = 3.
