Step-by-step explanation: The linear function that models Kate’s profit from her business is given by P(x) = 15x - 5x - 600 where x is the number of birdhouses sold.
The y-intercept of the function is -600. In this context, it means that Kate will have a loss of $600 if she does not sell any birdhouses.
The slope of the function is 10. In this context, it means that Kate will earn $10 for each birdhouse sold.
To earn at least $100 in profit, Kate needs to sell at least (100 + 600)/(15 - 5) = 80 birdhouses.
Hope this helps! :)