Certainly! Let's analyze the given problem step-by-step to derive the slope of a line parallel to the line given by the equation [tex]\( 7x - 6y = 7 \)[/tex].
1. Standard Form of a Line:
The given line equation is in the standard form [tex]\( Ax + By = C \)[/tex], where [tex]\( A = 7 \)[/tex], [tex]\( B = -6 \)[/tex], and [tex]\( C = 7 \)[/tex].
2. Slope of a Line:
In general, for any line given by [tex]\( Ax + By = C \)[/tex], the slope [tex]\( m \)[/tex] of the line can be found using the formula [tex]\( m = -\frac{A}{B} \)[/tex].
3. Calculate the Slope of the Given Line:
For the line [tex]\( 7x - 6y = 7 \)[/tex]:
- [tex]\( A = 7 \)[/tex]
- [tex]\( B = -6 \)[/tex]
Hence, the slope [tex]\( m \)[/tex] of the given line is:
[tex]\[
m = -\frac{A}{B} = -\frac{7}{-6} = \frac{7}{6} \approx 1.1666666666666667
\][/tex]
4. Slope of Parallel Line:
Lines that are parallel have the same slope. Therefore, the slope of any line parallel to the given line will be the same as the slope of the given line.
5. Conclusion:
Thus, the slope of a line parallel to the line [tex]\( 7x - 6y = 7 \)[/tex] is:
[tex]\[
1.1666666666666667
\][/tex]
So, the final answer is that the slope of a line parallel to the given line is approximately [tex]\( 1.1666666666666667 \)[/tex].
