Answer:
Step-by-step explanation:
We will use the following steps to solve this problem,
Step - (1).
Covert the equations into slope-intercept form.
Step - (2)
If the slopes of the two lines are equal, lines will be parallel.
[tex]m_1=m_2[/tex]
Step - (3)
If the slopes of the two lines are negative reciprocal, lines will be perpendicular.
[tex]m_1\times m_2=-1[/tex]
Line 1: 8x - 6y = -2
6y = 8x +2
y = [tex]\frac{4}{3}x+\frac{1}{3}[/tex]
Slope of line 1 = [tex]m_1=\frac{4}{3}[/tex]
Line 2: y = [tex]-\frac{3}{4}x-5[/tex]
Slope of line 2 = [tex]m_2=-\frac{3}{4}[/tex]
Line 3: 4y = -3x + 3
y = [tex]-\frac{3}{4}x+\frac{3}{4}[/tex]
Slope of line 3 = [tex]m_3=-\frac{3}{4}[/tex]
1). Since, [tex]m_1\times m_2=\frac{4}{3}\times (-\frac{3}{4})=-1[/tex]
Line 1 and line 2 are perpendicular.
2). Since, [tex]m_1\times m_3=\frac{4}{3}\times (-\frac{3}{4})=-1[/tex]
Line 1 and line 2 are perpendicular.
3). Since, [tex]m_2=m_3=-\frac{3}{4}[/tex]
Line 2 and line 3 are parallel.
