Linear equation formula
A linear equation describes a straight line. The slope-intercept form, y equals m x plus b, is the most common way to write it, showing the slope and the starting point at a glance.
- m = the slope, or steepness, of the line
- b = the y-intercept, where the line crosses the y-axis
- x, y = the coordinates of any point on the line
Slope-intercept form
In y = mx + b, the slope m tells you how steeply the line rises or falls: a positive slope climbs from left to right, a negative slope descends, and a zero slope is flat. The value b is the y-intercept, the height where the line crosses the vertical axis. Together they pin down the line completely.
Other useful forms
The same line can be written in point-slope form, y − y₁ = m(x − x₁), handy when you know one point and the slope. The standard form, Ax + By = C, is common in textbooks and useful for finding intercepts. All three describe the identical straight line.
A line with slope 2 crossing the y-axis at 3 is written y = 2x + 3. At x = 0, y = 3; at x = 4, y = 2(4) + 3 = 11. Plotting those points and connecting them draws the line.
Related tools
See the Slope Formula, or use the Slope Calculator to find m from two points.
FAQ
What is the slope-intercept form?
y = mx + b, where m is the slope and b is the y-intercept. It is the most common way to write a linear equation.
How do I find the slope from two points?
Divide the change in y by the change in x: m = (y₂ − y₁) / (x₂ − x₁). See the slope formula for details.