Question 548042
PART II
Let x be the number of hours worked. Let y be the cost, in $.
For plan (1) {{{y=1000+20x}}}
For plan (2) {{{y=25x}}}
Those are the expressions you can use to calculate cost (y) as a function of hours worked (x).
If the cost for plan 1 must be less than the cost for plan 2, we can set up the inequality
{{{1000+20x<25x}}}
We can solve that inequality by subtracting {{{20x}}} from both sides to get
{{{1000<5x}}} and then dividing both sides by 5 to get
{{{200<x}}}
So if you think the job will probably take more than 200 hours, use plan 1.
The lower hourly rate of $20 instead of $25, will more than offset the $1000 up-front fee, if the job takes more than 200 hours.
PART III
We have the functions from Part II above:
For plan (1) {{{y=1000+20x}}}
For plan (2) {{{y=25x}}}
Those are the equations for two straight lines.
The graph should look like this {{{graph(360,300,-80, 400,-1000,9000,25x,1000+20x)}}}