# Video: Writing Equations in the Slope-Intercept Form Using Given Information

In 2003, the population of a town was 45000 and the population has been growing linearly by 1700 people each year. Write an equation for the population, đť‘ť(đť‘ˇ), where đť‘ˇ is the number of years after 2003.

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### Video Transcript

In 2003, the population of a town was 45000 and the population has been growing linearly by 1700 people each year. Write an equation for the population đť‘ť of đť‘ˇ, where đť‘ˇ is the number of years after 2003.

Here, we have a linear equation, đť‘¦ equals đť‘šđť‘Ą plus đť‘Ź. We may recognize this from graphing, where đť‘š is the slope and đť‘Ź is the đť‘¦-intercept. But when thinking about this for a word problem, the đť‘¦-intercept would be considered the starting point, where the slope would represent the growth.

So letâ€™s begin plugging some things in. We are told to write an equation for the population đť‘ť of đť‘ˇ. So instead of đť‘¦, we need to use đť‘ť of đť‘ˇ. And it says đť‘ˇ is the number of years after 2003. So instead of đť‘Ą, we will be using đť‘ˇ.

So now letâ€™s think about đť‘š, the slope, the growth. It says it will be growing linearly by 1700 people each year. So we have 1700 each year, so times đť‘ˇ, plus our starting point. And the starting population was 45000. So we can either leave it like this, or we can switch the positions of the 1700 đť‘ˇ and the 45000. It doesnâ€™t matter. So here we would have our final answer.