A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point.

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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 this scenario?
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Mathematics

2 answers:

OleMash [197] · Answer 1 · 2021-12-22T18:19:30+03:00

Answer:

The graph that representss this scenario is attached.

Explanation:

You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.

1. Determine the expression that relates the variables.

a) The name of the variables is given:

x: number of solved puzzles

y: number of solved riddles

b) Point rules:

Each solved puzzle is worth two points: 2x

Each solved riddle is worth 1 point: 1y = y

Sum of points: 2x + y

The video game requires at least 4 points to advance: this means that the number of points must grater than or equal to 4 ⇒ 2x + y ≥ 4 .

In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.

2) Building the graph

Solve algebraically for y: y ≥ 4 - 2x

You want to draw the border line of the function, that is y = 4 - 2x

You have a linear function, so you need only two points to draw it. It is generally easier to work with the intercepts.

x-intercept (y = 0) ⇒ 2x + 0 = 4 ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)

y-intercept (x = 0) ⇒ 2(0) + y = 4 ⇒ y = 4 ⇒ point (0, 4).

In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.

Addtional constrains: x and y cannot be negative, so add the constrains:

x ≥ 0 and y ≥ 0

The set of solutions of y ≥ 4 - 2x is the same line y = 4 - 2x and the region over the line, so you have to shade that portion of the graph, but only in the first quadrant (since x and are greater than or equal to zero).

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