Question

Which choice has the same equation in both forms?

1.) standard form &

2.) slope intercept form


1.) 8x + 4y = 12 &

2.) y = -2x + 3


1.) 6x + 3y = 18 &

2.) y = 2x + 6


1.) 2x + 4y = 8 &

2.) y = -2x + 2


1.) 3x + 4y = 12 &

2.) y = ¾x + 3

Answer 1

8x + 4y = 12 & y = -2x + 3 are the same equations.

Explanation:

To know which choice has the same equation in both forms, we need to transform the standard form into the slope intercept form.

Then, solving for y in the first equation, we get:

`8x + 4y = 12\\8x + 4y - 8x = 12 -8x\\4y=12-8x\\(4y)/(4)=(12-8x)/(4) \\y=3 - 2x\\y=-2x+3`

It means that 8x + 4y = 12 & y = -2x + 3 are the same equations.

At the same way, we get that:

• 6x + 3y = 18 & y = 2x + 6 are not the same equation:

`6x + 3y = 18\\6x + 3y - 6x = 18-6x\\3y=18-6x\\(3y)/(3)=(18-6x)/(3) \\y=6 - 2x\\y=-2x+6`

• 2x + 4y = 8 & y = -2x + 2 are not the same equation:

`2x + 4y = 8\\2x + 4y -2x= 8-2x\\4y=8-2x\\(4y)/(4)=(8-2x)/(4)\\ y=2-(1)/(2)x`

• 3x + 4y = 12 & y = ¾x + 3 are not the same equation:

`3x + 4y = 12\\3x + 4y -3x= 12-3x\\4y=12-3x\\(4y)/(4)=(12-3x)/(4)\\ y=3-(3)/(4)x`