# Tomas wrote the equation y=3x+3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas's equation. Which equation could be Sandra's?

Nov 6, 2016

$4 y = 12 x + 3$

$12 x - 4 y + 3 = 0$

#### Explanation:

An equation can be given in many forms and still mean the same.

$y = 3 x + \frac{3}{4} \text{ }$ (known as the slope/intercept form.)

Multiplied by 4 to remove the fraction gives:

$4 y = 12 x + 3 \text{ "rarr 12x-4y = -3" }$ (standard form)

$12 x - 4 y + 3 = 0 \text{ }$ (general form)

These are all in the simplest form, but we could also have infinitely variations of them.

$4 y = 12 x + 3$ could be written as:

$8 y = 24 x + 6 \text{ " 12y = 36x +9, " } 20 y = 60 x + 15$ etc