Answer:
Slope of top rail f(x) is 7
Slope of top rail g(x) is 7
Top and bottom rails are parallel.
Step-by-step 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 Â Â Â Â Â 9 Â Â Â Â 43
2 Â Â Â Â Â 16 Â Â Â Â 50
3 Â Â Â Â Â 23 Â Â Â Â 57
To find the slope of top rail :
x     f(x)   Â
1 Â Â Â Â Â 9 Â Â Â Â
2 Â Â Â Â Â 16 Â Â Â Â
3 Â Â Â Â Â 23 Â Â Â Â
[tex](x_1,y_1)=(1,9)\\(x_2,y_2)=(2,16)\\Slope = m = \frac{y_2-y_1}{x_2-x_1}=\frac{16-9}{2-1}=7[/tex]
Slope of top rail f(x) is 7
To Find the slope of bottom rail:
x   g(x)
1 Â Â Â 43
2 Â Â Â 50
3 Â Â Â 57
[tex](x_1,y_1)=(1,43)\\(x_2,y_2)=(2,50)\\Slope = m = \frac{y_2-y_1}{x_2-x_1}=\frac{50-43}{2-1}=7[/tex]
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.
