Question

⦁ The equation (x + 5) + (y + 3) = 169 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.

Answer 1

Position (-5, -3)
Range 13

Answer 2

`y(x)=161-x`

Explanation:

The problem tell us that the position and range of the source of a radio signal is described by the next equation:

`(x+5)+(y+3)=169`

Let's isolate y and represent the previous equation the slope-intercept form:

`x+5+y+3=169\\x+y+8=169\\x+y=161\\y=161-x`

Now, we can say that the range of the signal as a function of the position is given by:

`y(x)=161-x`

Where:

`x=Position\\y=Range`

Analyzing the function we can conclude the next things:

• The slope is negative, which makes sense, the further away from the source, the signal will be weaker.
• The intercept is 161, this basically tell us that it is the max range of the signal
  `\forall x\geq0` because of a negative distance won't make any sense.
• The root of the function is 161, so for
  `x>161` the range of the signal will be lost.