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Writing Equations of Parallel Lines

Writing Linear Equations

Writing Equations of Parallel Lines 1.8 - Solution

Return to Writing Equations of Parallel Lines

If two lines are parallel they must have the same slope. We can read the $m$ -value if we rewrite the equations in slope-intercept form.

Line 1

4 x + y + 2 = 0

Write in slope-intercept form

LHS - 4 x = RHS - 4 x

y + 2 = - 4 x

LHS - 2 = RHS - 2

y = - 4 x - 2

The

m

-value is

- 4

.

Line 2

2 y + 4 = 8 x

Write in slope-intercept form

LHS - 4 = RHS - 4

2 y = 8 x - 4

LHS / 2 = RHS / 2

y = 4 x - 2

Line

2

has a

m

-value of

4

.

Line 3

8 x = 6 - 2 y

Write in slope-intercept form

LHS + 2 y = RHS + 2 y

2 y + 8 x = 6

LHS - 8 x = RHS - 8 x

2 y = - 8 x + 6

LHS / 2 = RHS / 2

y = - 4 x + 3

Line

3

, then, has the slope

m = - 4

.

Conclusion

Comparing the slope of the lines, we see that line $1$ and line $3$ have the same slope. Because these lines also have different $b$ -values ( $b = - 2$ and $b = 3$ ) they do not coincide. Line $1$ and line $3$ , are then, parallel.