Answer:
The correct option is D.
Step-by-step explanation:
The given equations are
[tex]4x=3y+23[/tex]
[tex]4y+3x=-19[/tex]
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
Rewrite the given equations is the slope intercept form.
[tex]y=\frac{4}{3}x-\frac{23}{3}[/tex]
[tex]y=-\frac{3}{4}x-\fra{19}{4}[/tex]
Therefore the slope of first line is [tex]\frac{4}{3}[/tex] and the slope of second line is [tex]-\frac{3}{4}[/tex].
[tex]m_1\times m_2=\frac{4}{3}\times =-\frac{3}{4}=-1[/tex]
Since the product of slopes of two perpendicular lines is -1, therefore we can say that both lines are perpendicular to each other. Option D is correct.
