Question

What is the slope of line PQ?
• -4
• 0
• 4
• undefined

What is the slope of line MN
• -2
• 2
• 0
• undefined

How are the two lines related ?
• the lines are parallel
• the lines are perpendicular
• the lines do not have slope
• the lines are coplanar

Answer 1

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Part a) Find the slope of line PQ

$P(-8,2)\ Q(4,2)$

substitute in the formula

$m=\frac{2-2}{4+8}$

$m=\frac{0}{12}=0$

Any line parallel to X-axis has slope equal to zero

so

the line PQ is parallel to the x-axis

therefore

the answer Part a) is

$0$

Part b) Find the slope of line MN

$M(8,6)\ N(8,-8)$

substitute in the formula

$m=\frac{-8-6}{8-8}$

$m=\frac{-14}{0}$

Anything divided by zero is undefined

m=undefined

therefore

the answer Part b) is

undefined

Part c) How are the two lines related ?

we know that

Any line perpendicular to X-axis has slope undefined

Because the term $(x2-x1)$ will always be zero

so

the answer Part c) is

the lines are perpendicular

Answer 2

Solpe of line $PQ\;\rm{is}\;0,$ slope of line $MN$ is undefined and Both lines are perpendicular to each other.

Step-by-step explanation:

Given: Image of two lines $\rm{PQ}\;\rm{and}\;MN$.

From the figure,

coordinates of $P(-8,2)\;\&\;Q(4,2)$.

Using the formula of slope of a line with coordinates $(x_{1} ,y_{1} )\;\&\;(x_{2} ,y_{2} )\;\rm{is}\;given\;by\;(m)=\frac{y_2-y_1}{x_2-x_1}$.

So, slope of line $PQ=\frac{2-2}{4+8}=0$

Therefore solpe of line $PQ\;\rm{is}\;0.$

Now,  coordinates of $M(8,6)\;\&\;N(8,-6)$.

slope of line $MN=\frac{-6-6}{8-8}=\frac{-12}{0}$ which is undefined.

Therefore, slope of line $MN$ is undefined.

Observing the given image: Both lines are perpendicular to each other.

Hence, Solpe of line $PQ\;\rm{is}\;0,$ slope of line $MN$ is undefined and Both lines are perpendicular to each other.

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