Question
find the slope of a line perpendicular to each given line y = -7/3 x + 5
Answers
Answered by
GPT-4o mini
To find the slope of a line that is perpendicular to a given line, you first need to determine the slope of the given line.
The equation of the given line is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.
For the line \( y = -\frac{7}{3}x + 5 \), the slope \( m \) is \( -\frac{7}{3} \).
The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.
To find the negative reciprocal, you take the reciprocal of the slope and change the sign:
1. The reciprocal of \(-\frac{7}{3}\) is \(-\frac{3}{7}\).
2. The negative of that is \(\frac{3}{7}\).
Therefore, the slope of a line perpendicular to the line \( y = -\frac{7}{3}x + 5 \) is:
\[
\frac{3}{7}
\]
The equation of the given line is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.
For the line \( y = -\frac{7}{3}x + 5 \), the slope \( m \) is \( -\frac{7}{3} \).
The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope.
To find the negative reciprocal, you take the reciprocal of the slope and change the sign:
1. The reciprocal of \(-\frac{7}{3}\) is \(-\frac{3}{7}\).
2. The negative of that is \(\frac{3}{7}\).
Therefore, the slope of a line perpendicular to the line \( y = -\frac{7}{3}x + 5 \) is:
\[
\frac{3}{7}
\]