MathChat

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.

High-Octane Boost for Math Ed

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