Learn Before
Verifying that and are Parallel
To determine whether the lines and are parallel, convert both equations to slope-intercept form and compare their slopes and -intercepts.
First equation: is already in slope-intercept form. The slope is and the -intercept is .
Second equation: Solve for by subtracting from both sides:
The slope is and the -intercept is .
Compare slopes and -intercepts:
- First line: ,
- Second line: ,
Because both lines have the same slope () but different -intercepts ( vs. ), the lines are parallel. When both lines are graphed on the same coordinate plane, they appear as two distinct lines that never cross. This demonstrates that by writing both equations in slope-intercept form, parallelism can be confirmed by inspection — without needing to graph the lines — simply by checking that the slopes match and the -intercepts differ.
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Ch.4 Graphs - Elementary Algebra @ OpenStax
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Learn After
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