To compare the two equations, we first need to rewrite them in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
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For the first equation: \[ -\frac{1}{2}x + y = 8 \] Rearranging gives: \[ y = \frac{1}{2}x + 8 \] Here, the slope \(m_1 = \frac{1}{2}\) and the y-intercept \(b_1 = 8\).
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For the second equation: \[ \frac{1}{2}y = \frac{1}{4}x - 4 \] Multiplying through by 2 to eliminate the fraction gives: \[ y = \frac{1}{2}x - 8 \] In this case, the slope \(m_2 = \frac{1}{2}\) and the y-intercept \(b_2 = -8\).
Now we can compare the two equations:
- Both equations have the same slope \(m = \frac{1}{2}\), which means they are parallel lines.
- However, they have different y-intercepts (8 and -8), so they do not intersect.
Given the analysis, the true statement among the provided options is:
The equations have the same slopes and are parallel lines.