Question

Which statement is true about the graphs of the two lines y = x + 2 and y = x ? The lines are perpendicular to each other because and are opposite reciprocals of each other. The lines are perpendicular to each other because 2 and are opposite reciprocals of each other. The lines are neither parallel nor perpendicular to each other because and are not opposite reciprocals of each other. The lines are neither parallel nor perpendicular to each other because 2 and are not opposite reciprocals of each other.

Answer 1

Answer: The answer is "the lines are parallel because both have same slope equal to 1"

Step-by-step explanation: The given equations are

$y=x+2,\\\\y=2.$

We are to find the relation between the above two lines.

We have

$y=x+2\\\\\Rightarrow y=1\times x+2,$

So the slope will be

$m_1=1.$

Also,

$y=x\\\\\Rightarrow y=1\times x+0,$

So the slope will be

$m_2=1.$

Therefore,

$m_1=m_2,$ which implies that the slope of the two lines are equal.

Thus, the given lines are parallel because both have same slope.

Answer 2

The lines y=x+2 and y=x are parallel, because they have the same slope.