Question

I need help with this question. IT IS NOT MULTICHOICE. again, IT ISNT MULTICHOICE. (brainliest, 12 pts)

Answer 1

Answer:

Part A) The given enrollment numbers as a pair of points are (0,900) and (3,1,500)

Part B) The slope of the line is $m=200\ \frac{students}{year}$ (see the explanation)

Part C) $P=200t+900$

Part D) $P=2,500\ students$

Step-by-step explanation:

Part A) Write the given enrollment numbers as a pair of points in the form (t,P)

Let

t ----> the number of years since 2009 (independent variable or input value)

P ---->the high school's student enrollment (dependent variable or output value)

we know that

For t=0 (year 2009) ----> P=900 students

so

The first ordered pair is (0,900)

For t=2012-2009=3 years ----> P=1,500 students

so

The second ordered pair is (3,1,500)

therefore

The given enrollment numbers as a pair of points are (0,900) and (3,1,500)

Part B) Find the slope of the line passing though the pair of points

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

(0,900) and (3,1,500)

substitute the values

$m=\frac{1,500-900}{3-0}$

$m=\frac{600}{3}$

$m=200\ \frac{students}{year}$

That means that the high school's student enrollment increase at rate of 200 students by year since 2009

Part C) Write an equation that relates the high school's student enrollment, P, to the number of years since 2009, t

we know that

The equation of a line in slope intercept form is equal to

$P=mt+b$

where

m is the slope

b is the P-intercept

In this problem we have

$m=200$

$b=900$ ---> represent the initial value ( value of P when the value of t is equal to zero)

substitute

$P=200t+900$

Part D) Predict the high school's enrollment in 2017

For t=2017-2009=8 years

substitute the value of t in the linear equation

$P=200(8)+900$

$P=2,500\ students$