Answer:
The correct option is 4.
Step-by-step explanation:
In the graph orange region represents the ways Janelle can win the beanbag toss game.
From the given graph it is clear that the related line passes through the points (2,5) and (10,0).
If a line passes through two points, then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of related line is
[tex]y-5=\frac{0-5}{10-2}(x-2)[/tex]
[tex]y-5=-\frac{5}{8}(x-2)[/tex]
Add 5 on both the sides.
[tex]y-5+5=-\frac{5}{8}(x)+\frac{5}{4}+5[/tex]
[tex]y=-\frac{5}{8}(x)+\frac{25}{4}[/tex]
The shaded region is above the line, so the sign of inequality is ≥.
The required inequality is
[tex]y\geq -\frac{5}{8}(x)+\frac{25}{4}[/tex]
Check the each point whether it satisfy the inequality of not.
In option (1), the given point is (7,1).
[tex]1\geq -\frac{5}{8}(7)+\frac{25}{4}[/tex]
[tex]1\geq 1.875[/tex]
This statement is false.
In option (2), the given point is (6,2).
[tex]2\geq -\frac{5}{8}(6)+\frac{25}{4}[/tex]
[tex]2\geq 2.5[/tex]
This statement is false.
In option (3), the given point is (5,3).
[tex]3\geq -\frac{5}{8}(5)+\frac{25}{4}[/tex]
[tex]3\geq 3.125[/tex]
This statement is false.
In option (4), the given point is (4,4).
[tex]4\geq -\frac{5}{8}(4)+\frac{25}{4}[/tex]
[tex]3\geq 3.75[/tex]
This statement is true. It means the point (4,4) describes a way Janelle can win the game. Therefore the correct option is 4.
