Question

What is the total cost of joining the club and playing 10 games during the year?

Answer 1

game (slope) Number of Games fee b=90. What is the total cost of joining the club and playing. 10 games during the year? 30x+90 y= y=30 (10) 730.
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Answer 2

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:

`y=mx+b`

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).

`\begin{gathered} y=mx+b \\ 120=m\cdot1+90 \\ m=120-90 \\ m=30 \end{gathered}`

The slope has a value of m=30.

Then, we have the equation as:

`y=30x+90`

We can find the cost of joining and playing 10 games by replacing x with 10 and calculating for y:

`\begin{gathered} y(10)=30(10)+90 \\ y(10)=300+90 \\ y(10)=390 \end{gathered}`

Answer: $390