Answer:
• Slope perpendicular to the line: 8/5
,
• Slope parallel to the line: –5/8
Explanation
Given
[tex]5x+8y=7[/tex]
To know the result, it is better if we work with the slope-intercept form:
[tex]y=mx+b[/tex]
Then, to get this kind of form we have to isolate y from the given equation:
[tex]8y=7-5x[/tex][tex]y=\frac{7-5x}{8}[/tex][tex]y=-\frac{5}{8}x+\frac{7}{8}[/tex]
Thus, in this case, m = –5/8 and b = 7/8.
Perpendicular lines have negative reciprocal lines:
[tex]m_2=-\frac{1}{m_1}[/tex]
where m₁ is the slope of line 1 and m₂ is the line perpendicular to line 1.
Then, replacing the values:
[tex]m_2=-\frac{1}{-\frac{5}{8}}[/tex][tex]m_2=\frac{8}{5}[/tex]
Finally, the slopes of parallel lines are the same, meaning:
[tex]m_2=m_1[/tex]
where m₁ is the slope of line 1 and m₂ is the line parallel to line 1.
