Tomas wrote the equation $y = 3 x + \frac{3}{4}$ $y=3x+3/4$ . 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?

Question

12135 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-06T12:25:02

$4 y = 12 x + 3$ $4y = 12x +3$

$12 x - 4 y + 3 = 0$ $12x-4y +3 = 0$

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

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

Multiplied by 4 to remove the fraction gives:

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

$12 x - 4 y + 3 = 0$ $12x-4y +3 = 0" "$ (general form)

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

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

$8 y = 24 x + 612 y = 36 x + 9, 20 y = 60 x + 15$ $8y = 24x +6" " 12y = 36x +9, " " 20y = 60x +15$ etc

Tomas wrote the equation y=3x+3/4y=3x+34y=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?