The lines represented by the equations 5y – 6x = –15 and y = x + 5 are

the same line?

perpendicular?

parallel?

neither parallel nor perpendicular?

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

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

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.

step-by-step explanation:

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step-by-step explanation: