Show all work as you solve the linear modeling problem below

Question

I'm not good at word problems, please help!

 

 

 There were 246 Apple stores worldwide in 2008 and 317 Apple stores worldwide in 2010. Write
a linear equation in slope-intercept form that models this growth. Let x stand for the number of
years after 2008 and let y = the number of Apple stores worldwide.

Answer 1

Hello Valerie,

If I were to come across this problem out in the wild, here is how I would solve it.

I would first find any key words that would help me solve the problem. There are several in this problem. I know it is a linear equation which right there mean we can use slope-intercept form, then it actual says we should use it.

 

So here are the formula for a linear equation in slope-intercept form:

y =mx + b

 

Next, I see that I need to find values for x, y, m, and b. The question goes on to say that x = years after 2008 and y = number of Apple stores worldwide.

 

I know have values of x and y. To visualize what I am doing I would probable graph the linear equation. I see two points to graph:

 

(x,y) = (year, # of Apple stores worldwide) or point 1 = (0, 246) and point 2 = (2, 317)

 

Now I can find m = "rise over run" where rise equals 317-246 = 71 and run equals 2-0= 2.

 

m = 71/2, 71 is a prime number so this is in simplest form.

 

So we have y = (71/2)x + b

 

Now I solve for "b" by plug in one of the points for x and y. I think you can do this part yourself. 

 

I get y = (71/2)x + 246.

 

Remember: Check by plugging in one of the points into the formula.

Answer 2

x = number of years since 2008

y = number of Apple stores in year x

 

Assuming that the relationship between x and y is linear, (0, 246) and          (2, 317) are two points on a line.

 

slope of line = (317-246)/(2-0) = 71/2 = 35.5

 

Equation of line:  y - 246 = 35.5(x - 0)

 

                                       y = 35.5x + 246