Parallelism Math Example 1

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

easy

Line

\ell_1

passes through

(0, 2)

and

(4, 6)

. Write the equation of a line

\ell_2

parallel to

\ell_1

passing through

(1, -3)

1
Step 1: Slope of $\ell_1$ : $m_1 = \dfrac{6-2}{4-0} = 1$ .
2
Step 2: Parallel lines have equal slopes, so $m_2 = 1$ .
3
Step 3: Point-slope form through $(1, -3)$ : $y + 3 = 1(x - 1) \Rightarrow y = x - 4$ .

Answer

y = x - 4

Two distinct lines in the same plane are parallel if and only if they have equal slopes. Here both lines have slope

1

but different

y

-intercepts (

2

and

-4

), confirming they never intersect.

About Parallelism

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

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