Standard Form to Slope-Intercept Form Calculator

Convert Ax + By = C into y = mx + b and instantly identify the slope and y-intercept.

Convert a linear equation
Enter the coefficients from Ax + By = C.

About standard form and slope-intercept form

A linear equation can describe the same straight line in several equivalent forms. Standard form is commonly written Ax + By = C, where A, B, and C are constants and x and y are variables. This arrangement is useful when coefficients are integers, when comparing equations in a system, and when finding intercepts. Slope-intercept form is written y = mx + b. It makes two important features visible immediately: m is the slope, and b is the point where the line crosses the vertical axis. Converting standard form to slope-intercept form means isolating y. Start with Ax + By = C, subtract Ax from both sides, and obtain By = -Ax + C. Then divide every term by B. The result is y = (-A/B)x + C/B. Therefore the slope is -A/B and the y-intercept is C/B. This calculator applies those rearrangement steps directly and displays decimal values without changing the line represented by the equation. The coefficient B must not be zero for this conversion. If B equals zero, the equation reduces to Ax = C, which represents a vertical line. A vertical line has an undefined slope and cannot be expressed as y = mx + b. Negative coefficients are valid, as are decimal coefficients. Keep each sign with its coefficient when entering the values; for example, enter -2 for B in 3x - 2y = 8. Slope tells how much y changes when x increases by one unit. A positive slope rises from left to right, a negative slope falls, and a zero slope is horizontal. The y-intercept provides a convenient first point for graphing. From that point, use the slope as rise over run to locate another point. Converting forms is therefore useful for graphing, checking algebra homework, comparing rates of change, and preparing equations for substitution. The displayed equation may include a plus sign before a negative intercept, such as y = 1.5x + -4. This is numerically identical to y = 1.5x - 4. The separate slope and intercept lines make the intended values unambiguous, while the direct format keeps automated calculation results consistent.

Conversion examples

These equations show how the coefficients determine slope and intercept.

Standard formSlope-intercept formKey values
2x + y = 5y = -2x + 5Slope -2; y-intercept 5
3x - 2y = 8y = 1.5x - 4Slope 1.5; y-intercept -4
-4x + 2y = 6y = 2x + 3Slope 2; y-intercept 3

How to convert standard form

  1. Read A, B, and C from the equation Ax + By = C, keeping every negative sign.
  2. Enter the three coefficients in their matching fields.
  3. Select Convert Equation to isolate y and calculate the slope and intercept.
  4. Use the displayed slope and y-intercept to graph or check the converted equation.

Standard form conversion FAQ

What is the conversion formula?

For Ax + By = C, divide after isolating y to get y = (-A/B)x + C/B. Thus the slope is -A/B and the y-intercept is C/B.

Why can B not equal zero?

When B is zero, the equation represents a vertical line of the form x = constant. Vertical lines have undefined slope, so they cannot be written in slope-intercept form.

Can the coefficients be negative or decimal?

Yes, both negative and decimal coefficients are valid. Enter the sign as part of each value so the calculator preserves the original equation.

How do I graph the converted equation?

Plot the y-intercept on the vertical axis first. Then interpret the slope as rise over run to find a second point and draw the line.

Are standard form and slope-intercept form equivalent?

Yes, the two forms describe exactly the same set of points when the algebraic operations are applied to both sides. They simply emphasize different properties of the line.