An architect needs to determine the slope between two points on a ski lift. The two points have been identified as (15, 35) and (195, 50), where x is the horizontal distance and y is the vertical distance from the bottom of the lift. Assuming the lift runs in a straight line, what is the slope of the line between the two points?

Question

anonymous · Answer

Okay. So you know how ordered pairs are set up, right? 

(x, y) 

So, for example, take a look at the FIRST ordered pair: (15, 35)

In this case...
X = 15
Y = 35

You see? 

~~~~~~~~~~~~~

Now, we have two ordered pairs. 

Here's the formula for finding the slope: 

$$\frac{ y_{1}-y_{2} }{x_{1}-x_{2} }$$

~~~~~~~~~~~~~~~

I'll walk you through this formula step by step. 

1. Look at our ordered pairs. 

(15, 35) and (195, 50) 


2. Find the FIRST Y, and subtract the SECOND Y. 

35 - 50 = -15

This is the NUMERATOR (top) of the slope fraction. 


3. Find the FIRST X, and subtract the SECOND X. 

15 - 195 = -180

This is the DENOMINATOR (bottom) of the slop fraction. 

~~~~~~~~~~~~~~

So now we have the slope fraction! 

$$\frac{ -15 }{ -180 }$$

which is the same as $$\frac{ 15 }{ 180 }$$

anonymous · Answer

Thanks!