Question

Are the lines parallel? Y=-3+2 and 3x+y=6

Answer 1

Hi there! I'll help you solve this problem!

In order for two lines to be parallel, their slopes should be equal.

We have two lines:

`\begin{cases}\sf{y=-3x+2}\\\sf{3x+y=6}}\end{cases}}`

Let's convert the second equation to slope-intercept (y = mx + b) form.

To do it, move 3x to the other side, using the opposite operation:

• 
  `\sf{y=6-3x}`
• 
  `\sf{y=-3x+6}`

Now the lines are:

`\begin{cases}\sf{y=-3x+2}\\\sf{y=-3x+6}\end{cases}`

Both lines have a slope of -3. which means their slope is the same.

Therefore, they are parallel.

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Best wishes!