To determine if the graphs of the lines are parallel, we need to compare their slopes. Lines are parallel if they have the same slope.
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The first line is already in slope-intercept form (y = mx + b): \[ y = 4x + 6 \] Here, the slope (m) is \(4\).
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For the second line, we need to rewrite the equation \(–15x + 3y = –45\) in slope-intercept form (y = mx + b). We can solve for \(y\): \[ 3y = 15x - 45 \quad \text{(adding 15x to both sides)} \] \[ y = 5x - 15 \quad \text{(dividing all terms by 3)} \] Here, the slope (m) is \(5\).
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Now, we compare the slopes of both lines:
- The first line has a slope of \(4\).
- The second line has a slope of \(5\).
Since the slopes \(4\) and \(5\) are not equal, the two lines are not parallel.
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