Question

Are the following pairs of equations equivalent? Be sure to show your work and use algebra to justify your reasoning.

y=3/2x+ 6 and 3x - 2y = 6

Answer 1

After transforming the second equation into slope-intercept form and comparing it to the first, it's determined that the equations y=3/2x+6 and 3x-2y=6 are not equivalent due to different y-intercepts.

Step-by-step explanation:

To determine if the equations y=3/2x+6 and 3x-2y=6 are equivalent, we need to manipulate one or both equations algebraically and see if we can transform one into the other.

Let's start by rearranging the second equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

1. First, we add 2y to both sides of the equation 3x - 2y = 6:
   3x = 2y + 6
2. Then we divide the entire equation by 2 in order to solve for y:
   y = 3/2x + 3

Now that we have both equations in the same form, we can easily compare them:

• The original equation is y = 3/2x + 6.
• The transformed equation is y = 3/2x + 3.

Because the y-intercepts are different (6 vs 3), the equations are not equivalent.