N Numeratibase

Free math tool

Line Equation Form Converter

Convert a linear equation into standard form, slope-intercept form, and point-slope form using one supported equation input.

Reset
2x - y = -3 y = 3x + 1 x = 4

Direct answer

Line forms

2x-y=-3 can be written as 2x - y = -3 and y = 2x + 3.

Standard form 2x - y = -3
Slope-intercept form y = 2x + 3
Point-slope form y - 3 = 2(x - 0)
Slope 2

Steps

  1. Start with 2x-y=-3.
  2. Move all x and y terms to the left and constants to the right to get 2x - y = -3.
  3. Clear denominators and simplify to standard form 2x - y = -3.
  4. Solve for y to get slope-intercept form y = 2x + 3.
  5. Use the y-intercept point (0, 3) to write point-slope form y - 3 = 2(x - 0).

Why it works

All linear equations in two variables describe the same line no matter which algebraically equivalent form you use. Rearranging the terms changes the presentation, not the line itself.

Common mistakes

  • Dropping a negative sign when moving terms across the equals sign.
  • Assuming every line can be written in slope-intercept form, even vertical lines.
  • Forgetting to simplify coefficients in standard form.

Worked examples

Convert 2x - y = -3

Standard form stays 2x - y = -3, and solving for y gives y = 2x + 3.

Convert x = 4

That is already a vertical line, so there is no slope-intercept form.

Practice

  • y = -x + 5
  • 3x + 2y = 12
  • y - 4 = 2(x - 1)