Parallelism Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Are the lines

y = 3x + 7

and

6x - 2y = 4

parallel? Justify your answer.

1
Step 1: Slope of the first line: $m_1 = 3$ .
2
Step 2: Rewrite the second: $-2y = -6x + 4 \Rightarrow y = 3x - 2$ , so $m_2 = 3$ .
3
Step 3: $m_1 = m_2 = 3$ but $y$ -intercepts differ ( $7 \neq -2$ ), so the lines are parallel.

Answer

Yes, they are parallel (

m_1 = m_2 = 3

, different intercepts).

Two distinct lines are parallel when they share the same slope but have different

y

-intercepts. Rewriting the second equation in slope-intercept form reveals slope

3

, confirming parallelism.

About Parallelism

Lines in the same plane that never intersect because they maintain a constant distance from each other.

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