# Precalculus : Linear Modeling

## Example Questions

### Example Question #1 : Linear Modeling

John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday for work. Each Monday he drives 350 miles to LaGrange. Once he arrives to his home away from home he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job.

Explanation:

The rate of change of his mileage is 700 per week (350 x 2=700 there and back). The rate of change is the same thing as slope. Since we are looking for equation an equation that models his odometer reading as a function of the number of weeks he has been driving we can extract the point (23 , 18600) since after 23 weeks his odometer read 18,600 miles. Now we will use the point slope formula:

distribute the right side

isolate y

### Example Question #2 : Linear Modeling

John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday. Each Monday he drives 350 miles to LaGrange. Once he arrives to his apartment he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job. Using the equation you just made, what is the y intercept or his original mileage before starting?

y intercept=16,100 miles

y intercept=186,000 miles

y intercept=169,900 miles

y intercept=153,800 miles