Answer:
m = [tex]-\frac{7}{8}[/tex]
Step-by-step explanation:
Finding the slope of the given line
We need to find the slope of this equation to find the slope of a line perpendicular to it. This means we must solve for y.
Start off by subtracting 8x from both sides of the equation to start isolating the variable y.
[tex]-7y=9- 8x[/tex]
Now solve for y by dividing both sides of the equation by -7.
[tex]y=\frac{9-8x}{-7}[/tex]
This can be broken into two parts by distributing the negative sign from the -7 into the 9 and -8x like so:
[tex]y=\frac{-9}{7} +\frac{8x}{7 }[/tex]
The slope of a line is the coefficient of x, so in this case the slope of the given line ([tex]-7y+8x=9[/tex]) is [tex]\frac{8}{7}[/tex].
Finding the slope of a line perpendicular to the given line
Two lines that are perpendicular would have opposite reciprocal slopes, which means the perpendicular slope would be the negative counterpart and would be flipped.
For example, if you have 2 as the slope of one of the perpendicular lines, the other line would be the opposite (-2) reciprocal ([tex]-\frac{1}{2}[/tex]).
Therefore, since we have the slope of one of the perpendicular lines (the given line), we would find the opposite reciprocal of it's slope to solve this problem.
Slope: [tex]\frac{8}{7}[/tex]
- Opposite: [tex]-\frac{8}{7}[/tex]
- Reciprocal: [tex]-\frac{7}{8}[/tex]
The slope of the line perpendicular to [tex]-7y+8x=9[/tex] is [tex]-\frac{7}{8}[/tex].
