Math
Slope Intercept Form Calculator
Enter a line as two points, a point and a slope, or in standard or general form and get y = mx + b with exact fractions. mathcheck also shows the slope, both intercepts, the point-slope, standard, and general forms, the angle the line makes with the x-axis, a graph, and the algebra step by step.
x-coordinate of the first point.
y-coordinate of the first point.
x-coordinate of the second point.
y-coordinate of the second point.
Try an example
Result
Slope-intercept form
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- Slope m
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- Y-intercept
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- X-intercept
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- Point-slope form
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- Standard form
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
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Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What is slope-intercept form?
How steep a line is: how much y changes for each step right in x.-A point where a graph crosses an axis. form is the equation of a line written as y = mx + b. The number m is the slope (rise over run) and b is the y-intercept, the y-value where the line crosses the y-axis. It is the most common way to write a line because you can read both the steepness and the starting point directly from the equation.
Three ways to find y = mx + b
| You know | Steps | Example |
|---|---|---|
| Two points | Find m from the points, then plug one point into y = mx + b and solve for b | (1, 2) and (5, 8): m = 6/4 = 3/2, b = 2 - (3/2)(1) = 1/2, so y = (3/2)x + 1/2 |
| A point and the slope | Substitute the point and slope, solve for b | m = -2 through (3, 1): 1 = -2(3) + b, so b = 7 and y = -2x + 7 |
| Standard form Ax + By = C | Move the x-term across, divide everything by B | 3x - 2y = -1 → -2y = -3x - 1 → y = (3/2)x + 1/2 |
| Form | Equation | Best when |
|---|---|---|
| Slope-intercept | y = mx + b | You want the slope and y-intercept at a glance |
| Point-slope | y - y1 = m(x - x1) | You know one point and the slope |
| Standard | Ax + By = C | Integer coefficients, intercepts, or systems of equations |
| General | Ax + By + C = 0 | Distance formulas and conic sections |
Why the calculator keeps fractions
Textbook answers keep m and b as reduced fractions such as 3/2 and 1/2, because decimals like 0.3333 are rounded and will not check exactly when you substitute a point back in. This page shows the exact fraction form first and the decimal version beside it.
How to use this calculator
- Choose how the line is given: two points, a point and a slope, or standard/general form.
- Enter the values. Slopes can be typed as fractions (3/2) or decimals (1.5).
- Read y = mx + b in the dark header, with the decimal version beside it when they differ.
- Use the grid for the slope, intercepts, and line type, and the list below it for the point-slope, standard, and general forms.
- Open Show the work to see how b was found.
How to read the answer
The equation y = mx + b tells you two things: m is how much y changes for each 1-unit increase in x, and b is the y-value when x = 0. A positive m rises to the right, a negative m falls, m = 0 is horizontal, and a vertical line has no slope-intercept form at all, so it is written as x = constant.
Common mistakes and edge cases
- Mixing up the order of subtraction: (y2 - y1) must go over (x2 - x1) in the same order, or the sign of the slope flips.
- Forgetting to divide the whole standard-form equation by B, not just the x-term, when isolating y.
- Writing y = mx + b for a vertical line. Two points with the same x-value give an undefined slope and the equation x = constant.
- Rounding the slope early. Keep 3/2 as a fraction until the final answer, or b will come out slightly wrong.
- Two identical points do not define a line; the calculator asks for two different points.
Worked examples
Two points, fraction slope
Line through (1, 2) and (5, 8)
Slope-intercept form
y = (3/2)x + 1/2
Point and negative slope
Slope -2 through (3, 1)
Slope-intercept form
y = -2x + 7
Standard form to y = mx + b
2x + 3y = 12
Slope-intercept form
y = (-2/3)x + 4
General form with decimals
0.5x - 0.25y + 1 = 0
Slope-intercept form
y = 2x + 4
Horizontal line
Line through (-3, 4) and (6, 4)
Slope-intercept form
y = 4
Vertical line has no y = mx + b
Line through (2, -1) and (2, 5)
Slope-intercept form
x = 2
Identical points
(4, 4) entered twice
Slope-intercept form
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Frequently asked questions
What do m and b stand for in y = mx + b?+
m is the slope, the change in y for each 1-unit change in x. b is the y-intercept, the value of y where the line crosses the y-axis (when x = 0).
How do I find b when I know the slope and a point?+
Substitute the point's x and y and the slope into y = mx + b, then solve for b: b = y - mx. For slope 2 through (3, 7), b = 7 - 2(3) = 1.
How do I convert Ax + By = C to slope-intercept form?+
Subtract Ax from both sides to get By = -Ax + C, then divide every term by B: y = (-A/B)x + C/B. The slope is -A/B and the y-intercept is C/B.
Can a vertical line be written in slope-intercept form?+
No. A vertical line has an undefined slope because the run is 0. It is written as x = constant, for example x = 2.
Why does the calculator show fractions instead of decimals?+
Fractions are exact. A slope of 1/3 written as 0.333 is rounded, and substituting a point back into the rounded equation will not check perfectly. The decimal version is shown next to the exact form for convenience.
What is the difference between slope-intercept form and point-slope form?+
Both describe the same line. Point-slope form y - y1 = m(x - x1) is written directly from a point and the slope; slope-intercept form y = mx + b is what you get after distributing and solving for y.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026