Slope Formulas and Forms of a Line
Compare the slope formula, point-slope form, slope-intercept form, standard form, and special horizontal and vertical lines.
These formulas move between two points, a slope, and several equivalent equations of the same straight line.
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6 formulas, different jobs
These formulas move between two points, a slope, and several equivalent equations of the same straight line.
Slope from Two Points
Use it when two points on a non-vertical line are known.
Slope-Intercept Form
Use it to read the slope and y-intercept immediately.
Point-Slope Form
Use it when one point and the slope are known.
Standard Form
Use it for integer coefficients and for both ordinary and vertical lines.
Horizontal Line
Use it when every point has the same y-coordinate.
Vertical Line
Use it when every point has the same x-coordinate.
Two points, three forms of one line
Use the points (2, 3) and (6, 11) to find the slope, then write the same line in point-slope, slope-intercept, and standard form.
- 1 · Find slope
- 2 · Point-slope
- 3 · Slope-intercept
- 4 · Standard
Common mistakes
- Subtracting the y-values in one order and the x-values in the opposite order.
- Confusing the y-intercept b with the x-coordinate of a known point.
- Trying to give a vertical line a finite slope.
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Slope formulas FAQ
Which form of a line should I use?
Use point-slope form with a point and slope, slope-intercept form when you need m and b, and standard form when integer coefficients or a vertical line matter.
Why is the slope of a vertical line undefined?
Its change in x is zero, so the slope formula would require division by zero.