Answer:
The lines are neither parallel nor perpendicular.
Therefore, we conclude that the statement ''neither parallel nor perpendicular'' is the correct answer.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
Given the line equations
5y – 6x = –15
y = x + 5
Analyzing the equation 5y – 6x = –15
Given the equation
5y – 6x = –15
writing in the slope-intercept form of the line equation
5y = 6x - 15
divide both sides by 5
[tex]y=\frac{6}{5}x-3[/tex]
comparing with the slope-intercept form y = mx+b of the line equation
Thus, the slope of the line 5y – 6x = –15 is:
m₁ = 6/5
Analyzing the equation y = x + 5
Given the equation
y = x + 5
comparing with the slope-intercept form y = mx+b of the line equation
Thus, the slope of the line y = x + 5 is:
m₂ = 1
Conclusion:
The slope of the line 5y – 6x = –15 is:
The slope of the line y = x + 5 is:
We know that when two lines are parallel, they have equal slopes
But
m₁ ≠ m₂
6/5 ≠ 1
As the m₁ and m₂ are not equal.
Hence, the lines are NOT parallel.
We know that when two lines are parallel, the product of their slopes is -1.
Let us check the product of two slopes m₁ and m₂
m₁ × m₂ = 6/5 × 1
= 6/5
As
m₁ × m₂ ≠ -1
Thus, the lines are not perpendicular.
In a nutshell,
The lines are neither parallel nor perpendicular.
Therefore, we conclude that the statement ''neither parallel nor perpendicular'' is the correct answer.
