This calculator converts an equation from standard form, Ax + By = C, into slope-intercept form, y = mx + b. Enter A, B and C and it shows the slope, the y-intercept and the x-intercept, with each algebra step, and it handles vertical lines where B is 0.
If you start from two points instead of an equation, the slope calculator gives the slope and line equation directly.
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How to convert standard form to slope-intercept form
The steps
Solve Ax + By = C for y.
Ax + By = C
By = −Ax + C
y = (−A ÷ B)x + (C ÷ B)
Where:
- m = −A ÷ B is the slope
- b = C ÷ B is the y-intercept
Intercepts from standard form
Set x = 0 to find the y-intercept, C ÷ B. Set y = 0 to find the x-intercept, C ÷ A. The calculator shows both.
When B is 0
If B = 0, the equation becomes Ax = C, so x = C ÷ A. This is a vertical line. It has no slope and cannot be written as y = mx + b.
When A is 0
If A = 0, the equation becomes By = C, so y = C ÷ B. This is a horizontal line with a slope of 0, and it has no x-intercept.
Worked examples
Example 1: 3x + 4y = 12
4y = −3x + 12
y = (−3 ÷ 4)x + 12 ÷ 4
y = (−3/4)x + 3
The slope is −3/4 = −0.75 and the y-intercept is 3. The x-intercept is 12 ÷ 3 = 4.
Example 2: 2x − 5y = 10
−5y = −2x + 10
y = (−2 ÷ −5)x + 10 ÷ (−5)
y = (2/5)x − 2
The slope is 2/5 = 0.4 and the y-intercept is −2. The x-intercept is 10 ÷ 2 = 5. Dividing by a negative number flips the signs, which is the most common place to make an error.
Example 3: A vertical line, 5x = 15
Here B = 0, so x = 15 ÷ 5 = 3. The line is vertical, the slope is undefined, and there is no y-intercept.
Frequently asked questions
How do you convert standard form to slope-intercept form?
Subtract Ax from both sides, then divide every term by B. The result is y = (−A ÷ B)x + C ÷ B.
How do you find the slope from standard form?
The slope is −A ÷ B. For 3x + 4y = 12 the slope is −3 ÷ 4.
What is the y-intercept in standard form?
Set x = 0 and solve for y, which gives C ÷ B. For 3x + 4y = 12 it is 12 ÷ 4 = 3.
Why does dividing by a negative number change the signs?
Every term on both sides is divided by the same negative number, so each term changes sign. In Example 2, dividing −5y = −2x + 10 by −5 gives y = (2/5)x − 2.
Can every line be written in slope-intercept form?
No. A vertical line has an undefined slope, so it can only be written as x = a number.