Question

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.)

Explanation:

Step1: Define the inequality

The total points from puzzles ($2x$) and riddles ($y$) need to be at least 4, so:
$2x + y \geq 4$

Step2: Rewrite in slope-intercept form

Isolate $y$ to identify the boundary line:
$y \geq -2x + 4$

Step3: Identify boundary line features

The boundary line is $y = -2x + 4$, which has a y-intercept at $(0,4)$ and x-intercept at $(2,0)$ (set $y=0$: $0=-2x+4 \implies x=2$). The inequality $\geq$ means the region above and including this line is shaded.

Step4: Match to the graph

The third graph has the line with y-intercept $(0,4)$, x-intercept $(2,0)$, and the area above the line shaded.

Answer:

The third graph (rightmost graph with boundary line $y=-2x+4$ and shaded region above the line)