To find the intercepts of a function we need to remember that:
• The x-intercepts happen when the value of the function is zero, then we equate the function to zero and solve for x.
,
• The y-intercepts happen when x=0, then we plug x=0 in the expression and the result is the intercept.
With this in mind we have that in this case the x intercept is:
[tex]\begin{gathered} 380-20x=0 \\ 20x=380 \\ x=\frac{380}{20} \\ x=19 \end{gathered}[/tex]
Therefore the x-intercept is 19.
The y-intercept is:
[tex]\begin{gathered} f(0)=380-20(0) \\ =380 \end{gathered}[/tex]
Therefore the y-intercept is 380.
Now we plot the intercepts and join them with a straignt line to get the graph:
The x-intercept means that it takes 19 years for there to be no trout in the lake. The y-intercept represents the number of trout that were in the lake at the beginning of the population decrease.
