How do I convert standard form to slope-intercept form?

Select Ax + By = C and enter its coefficients. For 2x + 3y = 6, use A = 2, B = 3 and C = 6. Dividing by B gives y = (−A/B)x + C/B, so the slope is −2/3 and the intercept is 2. The equation displays y = −0.6667x + 2; numeric rows show more digits.

How do I convert slope-intercept to standard form?

Select y = mx + b and enter m and b. Moving mx to the left gives −mx + y = b. For y = 2x + 1, the output is −2x + y = 1. This is an equivalent standard form with the y coefficient equal to 1; it does not reduce coefficients to a preferred integer sign convention.

Can I graph a line from its slope and y-intercept?

Yes. With m = 2 and b = −3, the line crosses the y axis at −3 and rises 2 units for each unit to the right. The graph uses a representative segment and the same scale on both axes. For several equations on the same axes or SVG/PNG export, use Function Plotter.

Can I enter point-slope or general form?

For y − y₁ = m(x − x₁), select Point + slope and enter m, x₁ and y₁. For a general equation Ax + By + D = 0, select standard form and enter C = −D. The tool does not accept an entire equation string or solve nonlinear equations.

What happens if B is zero in standard form?

When A is nonzero, Ax = C is the vertical line x = C/A, which has no slope-intercept form. When both A and B are zero, C = 0 describes every point and a nonzero C gives no solution. Each case receives its own explanation.

Slope-Intercept Form Calculator

Enter the coefficients of y = mx + b or Ax + By = C to see the line, its slope and its y-intercept. The results include slope-intercept, point-slope and standard forms. These are coefficient inputs: rearrange a written equation into the selected form before entering its numbers.

Line equation · slope = rise / run2slope63.43° · 200% grade

Mode

Given form

Slope m

Intercept b

Enter the coefficients of y = mx + b or Ax + By = C. Move a general equation into one of those forms first; this input does not parse an equation string.

Sloperise / run
2
Y-interceptb in y = mx + b
1
Angledegrees above horizontal, arctan of the slope
63.4349488229°
Percent gradeslope × 100
200%
Equationy = mx + b, to four places
y = 2x + 1
Point-slope formusing the first point, coefficients to four places
y - 1 = 2(x - 0)
Standard formAx + By = C, B normalized to 1; four places
-2x + y = 1
Perpendicular slopenegative reciprocal, −1 / m
-0.5
Pitchrise per 12 of run
24:12

The same line in several forms. Slope is rise divided by run. The angle is the arctangent of the slope, in degrees above horizontal, so 45 degrees is a slope of 1. Percent grade is the slope times 100, the number a road sign uses. Distance is the straight length between the two points, from Pythagoras. The equation is the slope-intercept form y = mx + b, with b where the line crosses the y axis. And a roof pitch is the same slope written as the rise per 12 of run, so 6:12 is a slope of 0.5, a 50% grade and an angle of 26.57 degrees. A vertical line has no slope at all: the run is 0, and the tool says so instead of printing infinity.

Common questions

How do I convert standard form to slope-intercept form?: Select Ax + By = C and enter its coefficients. For 2x + 3y = 6, use A = 2, B = 3 and C = 6. Dividing by B gives y = (−A/B)x + C/B, so the slope is −2/3 and the intercept is 2. The equation displays y = −0.6667x + 2; numeric rows show more digits.
How do I convert slope-intercept to standard form?: Select y = mx + b and enter m and b. Moving mx to the left gives −mx + y = b. For y = 2x + 1, the output is −2x + y = 1. This is an equivalent standard form with the y coefficient equal to 1; it does not reduce coefficients to a preferred integer sign convention.
Can I graph a line from its slope and y-intercept?: Yes. With m = 2 and b = −3, the line crosses the y axis at −3 and rises 2 units for each unit to the right. The graph uses a representative segment and the same scale on both axes. For several equations on the same axes or SVG/PNG export, use Function Plotter.
Can I enter point-slope or general form?: For y − y₁ = m(x − x₁), select Point + slope and enter m, x₁ and y₁. For a general equation Ax + By + D = 0, select standard form and enter C = −D. The tool does not accept an entire equation string or solve nonlinear equations.
What happens if B is zero in standard form?: When A is nonzero, Ax = C is the vertical line x = C/A, which has no slope-intercept form. When both A and B are zero, C = 0 describes every point and a nonzero C gives no solution. Each case receives its own explanation.

Double-precision geometry from your numbers. Equations round coefficients to four decimal places; other readings show up to twelve significant digits. This calculates a line's geometry, not structural capacity or construction compliance.