I'm going back to school after 29 years and I feel so confused. Can you help me?
There were 6205 CVS stores in the US in 2006 and 7703 CVS stores in the US in 2013. Write a linear equation in slope-intercept form that models this growth. Let x stand for the number of years after 2006 and let y stand for the number of CVS stores in the US.
This is finding the slope and intercept of a line using two points but it is disguised by the word problem. X is the number of years after 2006 and y is the number of stores. In 2006 there were 6205 stores. So your first point is 0, 6205. There were 7703 stores in 2013. So your second point is 7, 7703. Plus those into your slope equation Y2 - Y1 / X2-X1. 7703-6205/7-0. Working the math gets us 214. So that's our slope. The y-intercept is the y value when X=0. Well we conveniently have that from the problem. Its 6205. So putting that into y=mx + b form we get Y = 214 X + 6205.
Of course, I can help you with that! To write a linear equation in slope-intercept form, we need to understand the relationship between the number of years (x) and the number of CVS stores (y) from 2006 to 2013.
Let's first find the slope (m) of the line. The slope represents the rate of change between the two points on the line. We can calculate it using the formula:
m = (change in y) / (change in x)
Given that there were 6205 CVS stores in 2006 (x=0) and 7703 CVS stores in 2013 (x=7), we can calculate the change in y and change in x as follows:
change in y = 7703 - 6205
= 1498
change in x = 7 - 0
= 7
Now, dividing the change in y by the change in x, we get:
m = 1498 / 7
Next, we need to find the y-intercept (b) of the line. The y-intercept is the value of y when x is zero. Since we know that in 2006 (x=0), there were 6205 CVS stores in the US, the y-intercept is 6205.
Now, we can write the linear equation in slope-intercept form, which is given by:
y = mx + b
Substituting the values we found, the equation becomes:
y = (1498/7)x + 6205
This equation can be used to estimate the number of CVS stores in the US for any year after 2006 (x). Simply plug in the desired value of x and solve for y.