Explanation:
A perpendicular line will have the opposite and reciprocal slope.
The slope of the given line is -2.5, which can also be written as:
[tex]-2.5=-\frac{2}{5}[/tex]
A perpendicular line will have a slope of:
[tex]\frac{5}{2}=0.4[/tex]
Line A has this slope, so it's perpendicular.
Line B can be rewritten as:
[tex]\begin{gathered} -2x+5y=8 \\ 5y=2x+8 \\ y=\frac{2}{5}x+\frac{8}{5} \end{gathered}[/tex]
This line is not perpendicular.
Line D can be rewritten as:
[tex]\begin{gathered} 2y=5x+1.5 \\ y=\frac{5}{2}x+\frac{1.5}{2} \end{gathered}[/tex]
This line is perpendicular to the given line.
And line C has a slope of 2/5, so it's not perpendicular.
Answer:
Lines B and C are not perpendicular
