We have a graph that relates the number of games with the total yearly cost.
The graph only shows results for up to 6 games, so we have to find the equation of the line to extrapolate it to 10 games.
We can find the equation of the line in slope-intercept form:
[tex]y=mx+b[/tex]
where y is the yearly total cost and x is the number of games.
The y-intercept b is the value of y when x=0. We can see it in the graph: when x=0 (no games), the yearly cost is $90.
So b=y(0)=90.
We can find the slope in many ways now, but we will find it by replacing x and y with known values of a point of the graph, like (x,y)=(1,120), that is the point that indicates that 1 game (x=1) costs a total $120 (y=120).
[tex]\begin{gathered} y=mx+b \\ 120=m\cdot1+90 \\ m=120-90 \\ m=30 \end{gathered}[/tex]
The slope has a value of m=30.
Then, we have the equation as:
[tex]y=30x+90[/tex]
We can find the cost of joining and playing 10 games by replacing x with 10 and calculating for y:
[tex]\begin{gathered} y(10)=30(10)+90 \\ y(10)=300+90 \\ y(10)=390 \end{gathered}[/tex]
Answer: $390
