To determine if the graphs of the lines in the given pair are parallel, we need to find the slopes of both lines and compare them.
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First Line: The equation of the first line is given in slope-intercept form:
\[ y = 5x + 6 \]
The slope (m) of this line is 5.
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Second Line: The second line is given in standard form:
\[ -18x + 3y = -54 \]
To find the slope, we can convert this to slope-intercept form (y = mx + b). Start by isolating \(y\):
\[ 3y = 18x - 54 \] \[ y = 6x - 18 \]
The slope of the second line is 6.
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Comparison of Slopes: Now we compare the slopes:
- Slope of the first line: 5
- Slope of the second line: 6
Since the slopes are different (5 ≠ 6), the lines are not parallel.
Conclusion:
The graphs of the lines in the pair are not parallel because their slopes are different.