Question

The two lines y y = x and y = x + 1 are parallel lines.
True
False

Answer 1

By definition, the Slope-Intercept Form of the equation of a line is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

The equation of a line that passes through the Origin has the following form:

$y=mx$

Where "m" is the slope of the line.

In this case, you have the first line that passes through the Origin:

$y=x$

You can identify that its slope is:

$m_1=1$

You also know the second equation, which is written in Slope-Intercept form:

$y=x+1$

You can identify that:

$\begin{gathered} m_2=1 \\ b=1 \end{gathered}$

By definition, the slopes of parallel lines are equal. Then, since:

$m_1=m_2$

These lines are parallel.

The answer is: True.