To find a line that is parallel to the line \( y = 56x \) and goes through the point \( (12, 6) \), we need to remember that parallel lines have the same slope.
The slope of the line \( y = 56x \) is \( 56 \). Therefore, we need a line in the form:
\[ y = 56x + b \]
where \( b \) is a y-intercept that we need to determine using the point \( (12, 6) \).
We can substitute \( x = 12 \) and \( y = 6 \) into the equation to solve for \( b \):
\[ 6 = 56(12) + b \]
Calculating \( 56(12) \):
\[ 56 \times 12 = 672 \]
Now substitute back:
\[ 6 = 672 + b \]
To find \( b \):
\[ b = 6 - 672 = -666 \]
So, the equation of the line that is parallel to \( y = 56x \) and passes through the point \( (12, 6) \) is:
\[ y = 56x - 666 \]
Since this specific line does not appear in your options, let's check if any of the given lines have the correct slope and also pass through the point \( (12, 6) \).
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Option: \( y = -65x + 6 \)
- Slope: -65 (not parallel)
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Option: \( y = -\frac{6}{5}x + 6 \)
- Slope: -\(\frac{6}{5}\) (not parallel)
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Option: \( y = 56x - 4 \)
- Slope: 56 (parallel)
- Check if it passes through (12, 6):
\[ 6 = 56(12) - 4 \] \[ 6 = 672 - 4 = 668 \quad \text{(false)} \]
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Option: \( y = \frac{5}{6}x - 4 \)
- Slope: \(\frac{5}{6}\) (not parallel)
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Option: \( y = 56x + 6 \)
- Slope: 56 (parallel)
- Check if it passes through (12, 6):
\[ 6 = 56(12) + 6 \] \[ 6 = 672 + 6 = 678 \quad \text{(false)} \]
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Option: \( 6y = 5x \)
- Rearranging gives \( y = \frac{5}{6}x \), slope = \(\frac{5}{6}\) (not parallel).
From the analysis above, none of the provided lines are parallel and pass through the point (12, 6). The closest one that is parallel is \( y = 56x - 4 \), but it does not pass through (12, 6).
So the best answer in terms of being parallel would be: \( y = 56x - 4 \) if referring just to parallelism. If strictly needing to satisfy point (12, 6), check for correct lines or recheck options.
1 answer