Algebraic esimation

Question

in a counry the number of students who completed high school and enrolled in college the same year increased from 1.3 millions in 2004 to 1.8 million in 2008. Find an equation for the line including the given data points. Let x represent the number of years after 2000 and y the number of recent high school graduates who enrolled in college that year. estimate the number of high school graduates who enrolled in college in 2006 and 2015

Answer 1

To find the equation of the line use RISE over RUN-----> Change in Y value divided by change in X value

 

your X values are the years after 2008,  while Y are the # of students

so your x axis should be labeled 0-15

 

change in Y  = second Y value - first Y value

change in X = second X value - first X value

 

1,800,000-1,300,000 / 8-4 --->  500,000/4 ---->125000 is the slope(m) of your line. 

then we must find the y intercept (b). In this graph the y-intercept is the value of students the year 2000.

Use the point slope formula y-y1=m(x-x1) ....we can use the given data to plug in points for (x1,y1). 

Using 1,300,000 for y1  and 4 for x1 and 125000 for m

y-(1300000)=125000(x-4)      <------dont forget to distribute 125000 on x and 4

y-1,300,000=125000x-500,000

y=125,000x-500,000+1,300,000

y=125,000x-800,000             <-----------now our equation is in y=mx+b form where b=800,000

 

plugging in any value for x (0-15) should give us the value of students for the corresponding year.

 

example: when x=15 this means year 2015.   y=125,000(15)+800,000 = 2,675,000 students

 

that should be the correct answer for students in the year 2015. for the year 2006, just use x=6 in the preceding equation.

 

Answer 2

     Since the x represents the years after 2000, you have the points (4,1,300,000) and (8, 1800000). Use the slope formula to get

500,000/4 which is 125,000.

I'll use y=mx +b to complete the problem. Plug in the slope and either point to get

1300000 = 125,000 (4) + b

1300000 = 500,000 + b

800,000 = b

So your equation to make estimates is y = 125,000 x + 800,000. Before we proceed, check to see if (8,  1800000) satisfies this just to make sure we have the right equation. So 1800000 = 125,000 (8) + 800,000 ? The answer is correct therefore the equation is correct.

 

So we can use this to estimate any year's student population. 2006 is x=6 and 2015 is x=15. plug them into your equation and get your estimate based on your 2 years of data.