# Problem Solving With Linear Functions Key

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In this section, we will explore examples of linear function models.How can they calculate how much they will charge for an evening of babysitting?Emily is a college student who plans to spend a summer in Seattle.The rate of change is constant, so we can start with the linear model $$M(t)=mt b$$.Then we can substitute the intercept and slope provided.To find the x-intercept, we set the output to zero, and solve for the input.$\begin 0&=−400t 3500 \ t&=\dfrac \ &=8.75 \end$ The x-intercept is 8.75 weeks.The amount of money she has remaining while on vacation depends on how long she stays.We can use this information to define our variables, including units. The problem should list the Y- intercept, a starting amount of something and a slope, or a rate of change. You can tell that you need to create a linear equation by the information the problem gives you.

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