Solved on Feb 12, 2024

Redefine the problem: Skateboard shop gets 92 wheels, puts 4 per board. Write a function g(x)g(x) to describe the number of wheels left after assembling xx boards.

STEP 1

Assumptions
1. Boyd starts with 92 new skateboard wheels.
2. Each skateboard requires 4 wheels.
3. The function g(x)g(x) represents the number of wheels left after assembling xx skateboards.
4. The function will be linear since the number of wheels decreases by a constant amount for each skateboard assembled.

STEP 2

Determine the initial number of wheels before assembling any skateboards. This is the yy-intercept (bb) of the linear function.
b=92b = 92

STEP 3

Determine the slope (mm) of the function, which represents the change in the number of wheels for each skateboard assembled.
Since 4 wheels are used for each skateboard, the number of wheels decreases by 4 for each skateboard assembled, so m=4m = -4.

STEP 4

Write the linear function in the form g(x)=mx+bg(x) = mx + b using the determined slope and yy-intercept.
g(x)=4x+92g(x) = -4x + 92
This function represents the number of new wheels Boyd has left after assembling xx skateboards.

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