Standard Form to Slope-Intercept Form

Convert Ax + By = C to y = mx + b. Enter A, B, and C to find the slope and y-intercept.

Enter Standard Form: Ax + By = C

2x + 3y = 12

Result

Slope-Intercept Form
y = -0.666667x + 4
Standard Form2x + 3y = 12
Slope (m)-0.666667
Slope as Fraction-2/3
Y-Intercept (b)4
X-Intercept6

Step-by-Step Solution

Ax + By = C => y = (-A/B)x + (C/B)

Understanding the Conversion

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Converting between these forms is a fundamental algebra skill.

Linear Equation Forms

Standard Form

Both variables on one side, constant on the other. A, B, C are typically integers.

Ax + By = C

Slope-Intercept Form

Solved for y. Slope (m) and y-intercept (b) are directly visible.

y = mx + b

Conversion Formula

Divide through by B and isolate y to convert between forms.

m = -A/B, b = C/B

Step-by-Step Method

  1. Start with the standard form: Ax + By = C.
  2. Subtract Ax from both sides: By = -Ax + C.
  3. Divide everything by B: y = (-A/B)x + (C/B).
  4. The slope is m = -A/B and the y-intercept is b = C/B.

Important Notes

  • If B = 0, the equation represents a vertical line (x = C/A), which has undefined slope and cannot be written in slope-intercept form.
  • The slope m tells you how much y changes for each unit increase in x.
  • The y-intercept b is the point where the line crosses the y-axis (x = 0).
  • A positive slope means the line goes upward; a negative slope means it goes downward.