How do you show that the slope of {(y=at+b),(x=ct+d):} is a/c?

1 Answer
Dec 18, 2015

Please see the explanation below

Explanation:

Each equation is defined using the independent variable t

As t changes x and y change accordingly.

Both x and y are linear functions

For y it is a line with slope a

We can write this as follows (\Delta y)/(\Delta t)=a

Solving for \Delta y

\Delta y=a\Deltat

For x it is a line with slope c

Proceeding as before we have

(\Deltax)/(\Deltat)=c

Solving for \Deltax

\Deltax=c\Deltat

The slope of the overall function is

(\Deltay)/(\Deltax)

Therefore

(\Deltay)/(\Deltax)=(a\Deltat)/(c\Deltat)=a/c

NOTE: \Delta means "change in"