### How to Convert a Linear Equation from Standard Form to Slope-Intercept Form

Suppose you’re given a linear equation in standard form and you need to convert it to slope-intercept form. You’ll be amazed how fast you can do this, if you know the “trick” I’m showing you here.

First, let’s review the key info from my post: **How to Transform from Standard Form to Slope-Intercept Form**.

That post shows how to pull out the the slope and y-intercept from a linear equation in standard form.

Remember that standard form is **Ax + By = C**, where A, B, and C are constants (numbers).

Given the equation in standard form, take note of the values of A, B, and C.

For example, in the equation, –** 12x + 3y = – 9**, **A = – 12, B = 3, and C = – 9**

Then, based on the info in yesterday’s post, we get the slope by making the fraction: **– A/B**.

And we get the y-intercept by making the fraction: **C/B**

New info for today: once you have the slope and y-intercept, just plug them in for **m** and **b** in the general slope-intercept equation: **y = mx + b**

Here’s the whole process, demonstrated for two examples.

Ex. 1: Given, **8x + 2y = 12**, A = 8 B = 2, C = 12.

So the slope = – A/B = – 8/2 =** – 4**. y-intercept = 12/2 = **6**

So the slope-intercept form is this: ** y = – 4x + 6**

Ex. 2: Given, **– 5x + 3y = – 9**, A = – 5, B = 3, C = – 9.

So the slope = – A/B = **5/3**, y-intercept = – 9/3 = **– 3**

So the slope-intercept form is this: **y = 5/3x – 3**

Now “give it a roll.” Once you get the hang of this, try the process without writing down a single thing. You might get a pleasant jolt of power when you see that you can do this conversion in your head.

**Conversion Problems** (Answers at bottom of post)

1) – 4x + 2y = 14

2) 20x – 5y = – 15

3) – 21x – 7x = 35

4) – 18x + 6y = – 21

5) 17x + 11y = 22

6) – 7x + 11y = – 44

7) 36x – 13y = – 52

8) – 8x + 5y = – 17

**Answers**

1) y = 2x + 7

2) y = 4x + 3

3) y = – 3x – 5

4) y = 3x – 7/2

5) y = – 17/11x + 2

6) y = 7/11x – 4

7) y = 36/13x + 4

8) y = 8/5x – 17/5