To identify which two lines are parallel, we need to look for lines that have the same slope. The slope can be identified from the equation of the line in the slope-intercept form \(y = mx + b\), where \(m\) is the slope.
Let's analyze the given lines:
-
\(y = 23x - 6\) and \(y = -32x - 6\)
- Slopes: 23 and -32 (not parallel)
-
\(y = \frac{2}{3}x - 6\) and \(y = -\frac{3}{2}x - 6\)
- Slopes: \(\frac{2}{3}\) and \(-\frac{3}{2}\) (not parallel)
-
\(y = 13x + 4\) and \(y = 13x + 4\)
- Both have slope: 13 (parallel)
-
\(y = -\frac{1}{2}x + 6\) and \(y = \frac{1}{2}x - 8\)
- Slopes: -\(\frac{1}{2}\) and \(\frac{1}{2}\) (not parallel)
-
\(y = 12x + 3\) and \(y = 12x - 5\)
- Both have slope: 12 (parallel)
The two pairs of parallel lines are:
- \(y = 13x + 4\) and \(y = 13x + 4\)
- \(y = 12x + 3\) and \(y = 12x - 5\)
Since we need to identify two lines that are parallel, the answer is confirmed by checking the first pair listed above in the list. The repeating line does not constitute a pair of distinct lines, so overall there are two different pairs of parallel lines, but the essential answer for identifying parallel lines is:
\(y = 13x + 4\) and \(y = 12x + 3\) with their respective repeats.
1 answer