Line 1 and Line 4 are parallel lines
Solution:
General equation of a line:
y = mx + c
where m is the slope and c is the y-intercept of the line.
To find the slope of each line:
Line 1: [tex]y=-\frac{3}{4} x-6[/tex]
Slope [tex](m_1)=-\frac{3}{4}[/tex]
Line 2: [tex]y-7=-4(x+9)[/tex]
[tex]y-7=-4x-36[/tex]
Add 7 on both sides, we get
[tex]y=-4x-29[/tex]
Slope [tex](m_2)=-4[/tex]
Line 3: [tex]y=-2 x+6[/tex]
Slope [tex](m_3)=-2[/tex]
Line 4: [tex]x+\frac{4}{3} y=-5[/tex]
Subtract x from both sides, we get
[tex]\frac{4}{3} y=-x-5[/tex]
Multiply by [tex]\frac{3}{4}[/tex] on both sides, we get
[tex]y=-\frac{3}{4}x-\frac{15}{4}[/tex]
Slope [tex](m_4)=-\frac{3}{4}[/tex]
Two lines are parallel, if their slopes are equal.
From the above slopes,
[tex]m_1=m_4[/tex]
Therefore Line 1 and Line 4 are parallel lines.
