Only the first graph represents the given situation. The correct option is A.
Given:
- A college student has two different jobs.
- Her combined work schedules consist of no more than 48 hours in one week.
To find:
The graph that represents the solution set for all possible combinations of the number of hours she worked at her first job and the number of hours she worked at her second job, in one week.
Explanation:
Let [tex]x[/tex] be the number of hours she worked at her first job and [tex]y[/tex] be the number of hours she worked at her second job, in one week.
Her combined work schedules consist of less than or equal to 48 hours in one week. So,
[tex]x+y\leq 48[/tex]
The number of hours cannot be negative.
[tex]y\geq 0[/tex]
[tex]x\geq 0[/tex]
The related equation is [tex]x+y=48[/tex].
At [tex]x=0[/tex],
[tex]0+y=48[/tex]
[tex]y=48[/tex]
The y-intercept is [tex](0,48)[/tex].
At [tex]y=0[/tex],
[tex]x+0=48[/tex]
[tex]x=48[/tex]
The x-intercept is [tex](48,0)[/tex].
Check the inequality for [tex](0,0)[/tex].
[tex]0+0\leq 48[/tex]
[tex]0\leq 48[/tex]
The above statement is true. It means [tex](0,0)[/tex] is included in the shaded region.
Therefore, the correct option is A.
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