Answer:
[tex]y(x)=161-x[/tex]
Step-by-step explanation:
The problem tell us that the position and range of the source of a radio signal is described by the next equation:
[tex](x+5)+(y+3)=169[/tex]
Let's isolate y and represent the previous equation the slope-intercept form:
[tex]x+5+y+3=169\\x+y+8=169\\x+y=161\\y=161-x[/tex]
Now, we can say that the range of the signal as a function of the position is given by:
[tex]y(x)=161-x[/tex]
Where:
[tex]x=Position\\y=Range[/tex]
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 [tex]\forall x\geq0[/tex] because of a negative distance won't make any sense.
- The root of the function is 161, so for [tex]x>161[/tex] the range of the signal will be lost.
