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

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 $\frac{\setminus \Delta y}{\setminus \Delta t} = a$

Solving for $\setminus \Delta y$

$\setminus \Delta y = a \setminus \Delta t$

For $x$ it is a line with slope $c$

Proceeding as before we have

$\frac{\setminus \Delta x}{\setminus \Delta t} = c$

Solving for $\setminus \Delta x$

$\setminus \Delta x = c \setminus \Delta t$

The slope of the overall function is

$\frac{\setminus \Delta y}{\setminus \Delta x}$

Therefore

$\frac{\setminus \Delta y}{\setminus \Delta x} = \frac{a \setminus \Delta t}{c \setminus \Delta t} = \frac{a}{c}$

NOTE: $\setminus \Delta$ means "change in"