a video game requires at least 4 points to advance. each solved puzzle is worth two points. each solved…

a video game requires at least 4 points to advance. each solved puzzle is worth two points. each solved riddle is worth 1 point. if x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

a video game requires at least 4 points to advance. each solved puzzle is worth two points. each solved riddle is worth 1 point. if x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

Answer

Explanation:

Step1: Set up the inequality

Since each solved puzzle ($x$) is worth 2 points and each solved riddle ($y$) is worth 1 point, and at least 4 points are required to advance, the inequality is $2x + y\geq4$.

Step2: Rewrite in slope - intercept form

Subtract $2x$ from both sides to get $y\geq - 2x + 4$. The boundary line is $y=-2x + 4$, which has a $y$-intercept of 4 and a slope of - 2. Since the inequality is $\geq$, the boundary line is solid and the region above the line is shaded.

Answer:

The graph with a solid line $y = - 2x+4$ and the region above the line shaded.