How to Convert Point-Slope Form (Standard & Slope-Intercept)

Once you’ve written a line in point-slope form, converting it into slope-intercept or standard form is just a little algebra. This guide covers both conversions with clear steps and worked examples.

Start With Point-Slope Form

We’ll convert the same line throughout, so you can see how the forms relate. Start with:

y − 2 = 3(x − 1)

Convert Point-Slope to Slope-Intercept Form (y = mx + b)

Steps

Distribute the slope across the parentheses, then solve for y by itself. That’s all it takes.

Worked Example

Distribute the 3: y − 2 = 3x − 3. Then add 2 to both sides:

y = 3x − 1

Now the slope (3) and the y-intercept (−1) are easy to read.

Convert Point-Slope to Standard Form (Ax + By = C)

Steps

The tidy way is to first reach slope-intercept form, then move the x term across so the variables sit together. Standard form wants integer coefficients with A positive, so clear fractions if you have any.

Worked Example

From y = 3x − 1, subtract 3x from both sides to get −3x + y = −1. Since A should be positive, multiply the whole equation by −1:

3x − y = 1

If the slope had been a fraction like 3/4, you’d multiply every term by 4 first to clear it before finishing.

Quick Reference Table

Check Your Conversion

The calculator lists point-slope, slope-intercept, and standard form together, so it’s a fast way to confirm your algebra. If you want a refresher on writing point-slope form first, see the three-step method, and to compare forms read point-slope vs slope-intercept.