Question

Can someone help with this question?✨

Answer 1

`y=700x+48000`

`52,200`

Explanation:

Generally for a linear equation you use the slope-intercept form:
`y=mx+b`

In this form,
`m=\text{slope},\ b=\text{y-intercept}`

The y-intercept is just when x=0, so it can be seen as a "starting point". in this case the initial population was 48,000 so we know that:
`b=48000`

The slope is just how much y-changes as x increases by one, and in this case our "x" will represent how many years it's been since 2003. So the slope will represent how much the population increases each year, and this is given in the word problem as 700 people each year.

So now we have the equation:
`y=700x+48000`

From 2003 to 2009, 6 years have passed meaning the population is the y-value when x=6:
`y=700(6)+48000\\y=52,200`