Answer: Line joining ordered pairs (0, 10) and (15, 0) and Shade the portion of the graph below this line which lies within the first quadrant.
Step-by-step explanation:
Here, The club charges $y an hour for each child and $x an hour for each adult.
And, according to the question,
In the family 3 children and 2 adults visited a health club such that the family does not want to spend more than $30 an hour at the health club.
That is, [tex]2x + 3y\leq 30[/tex]
Which is the required inequality.
Since at origin, [tex]2\times 0 + 3\times \leq 30[/tex] (true)
That is, the inequality must contains the origin.
Therefore, shaded region will occur below the line.
Also, x-intercept of the given line is (15,0)
And, y-intercept of the given line is (0,10)
Thus the line will join the order pairs (15,0) and (0,10)
Also, [tex]x\geq 0[/tex] and [tex]y\geq 0[/tex] ( because charges can not be negative)
Therefore the shaded region will only contain the first quadrant.
