Question

Which choice has the same equation in both forms?

Answer 1

Answer:

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

Step-by-step 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:

$8x + 4y = 12\\8x + 4y - 8x = 12 -8x\\4y=12-8x\\\frac{4y}{4}=\frac{12-8x}{4} \\y=3 - 2x\\y=-2x+3$

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:

$6x + 3y = 18\\6x + 3y - 6x = 18-6x\\3y=18-6x\\\frac{3y}{3}=\frac{18-6x}{3} \\y=6 - 2x\\y=-2x+6$

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

$2x + 4y = 8\\2x + 4y -2x= 8-2x\\4y=8-2x\\\frac{4y}{4}=\frac{8-2x}{4}\\ y=2-\frac{1}{2}x$

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

$3x + 4y = 12\\3x + 4y -3x= 12-3x\\4y=12-3x\\\frac{4y}{4}=\frac{12-3x}{4}\\ y=3-\frac{3}{4}x$