Answer:
- The graph that representss this scenario is attached.
Step-by-step 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
- 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).
The resulting graph is attached.