Question

A hand rail is installed along the stairs OT

house as shown in the figure. The table shows the
distance, in inches, of the top rail f(x) and bottom
rail g(x) from the floor for the middle of each
numbered stęp x. Determine the slope of each rail.
Are the top and bottom rails parallel?
x f(x) g(x)
1 9 43
2
16
50
3
3
23
57

Answer 1

Slope of top rail f(x) is 7

Slope of top rail g(x) is 7

Top and bottom rails are parallel.

Explanation:

The table shows the distance, in inches, of the top rail f(x) and bottom rail g(x) from the floor for the middle of each numbered stęp x.

x f(x) g(x)

1 9 43

2 16 50

3 23 57

To find the slope of top rail :

x f(x)

1 9

2 16

3 23

`(x_1,y_1)=(1,9)\\(x_2,y_2)=(2,16)\\Slope = m = (y_2-y_1)/(x_2-x_1)=(16-9)/(2-1)=7`

Slope of top rail f(x) is 7

To Find the slope of bottom rail:

x g(x)

1 43

2 50

3 57

`(x_1,y_1)=(1,43)\\(x_2,y_2)=(2,50)\\Slope = m = (y_2-y_1)/(x_2-x_1)=(50-43)/(2-1)=7`

Slope of top rail g(x) is 7

We know that if the slopes of two lines are equal then are said to be parallel lines

Since the slopes of both the rail are equal . So, Top and bottom rails are parallel.