Question

Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?y = -x + 11, 2y = -2x + 22

Answer 1

Given

The lines,

$\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}$

To find:

Whether the lines are perpendicular, coinciding, intersecting or parallel?

Explanation:

It is given that,

$\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}$

That implies,

Since the slope of the two lines are,

$\begin{gathered} m_1=-1 \\ m_2=\frac{-2}{2}=-1 \\ \therefore m_1=m_2 \end{gathered}$

Hence, the two lines are parallel.