Question

Identify which lines are parallel

Answer 1

The parallel lines are:

• 
  `y = 4` and
  `y = 3`
• 
  `y = 3x + 4` and
  `y = 3x`

`\boxed{\bold{Explanation}}`

Remember that the equation of the line is expressed:

`y \: = \: mx \: + \: b`

Where:

• 
  `m` is the slope
• 
  `b` is the ordinate of origin

Now that we know this, let's remember that for two lines to be parallel they must have the same slope (m).

We see equality of the slpoes,

`y \: = \: \bold{ 3}x \: + \: 4 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇝ \: m \: = \: 3 \\ y \: = \: \bold{3}x`

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`y \: = \: 4 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇝ m \: = \: 0\\ y \: = \: 3`