Answer:
[tex]y=-3,250t+25,000[/tex]
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope of unit rate of the linear equation
b is the y-intercept or initial value of the linear equation
Let
t ----> the number of years since 2011
y --->the car's value
In this problem the year 2011 represent t=0
so
the year 2015, represent t=4 years (2015-2011)
we have the ordered pairs
(0,25,000) ----> represent the y-intercept
(4,12,000)
Find the slope m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{t2-t1}[/tex]
substitute the values
[tex]m=\frac{12,000-25,000}{4-0}[/tex]
[tex]m=\frac{-13,000}{4}[/tex]
[tex]m=-\$3,250\ per\ year[/tex] ---> is negative because is a decreasing function
we have
[tex]b=\$25,000[/tex] ----> value of y when the value of x is equal to zero (initial value)
substitute the given values
[tex]y=-3,250t+25,000[/tex]
Answer:
y = -3250t + 25000
Explanation:
Assuming the years between 2011-2015 to be a straight line
We know that, for a straight line, y = mx + c,
Where, m is slope of unit rate
c is the y-intercept
Consider t to be the no. of years since 2011 and y to be the car’s value
So, for 2011, t=0
And for 2015, t=4 (2015-2011)
Finding the slope m
m =[tex]\frac{y^{2}-y 1}{t 2-t 1}[/tex]
m =[tex]\frac{12000-25000}{4-0}[/tex]
m = - [tex]\frac{13000}{4}[/tex]= -3250 per year (negative because it is a decreasing function)
We have, c = 25000
Substituting the values in the straight line equation,
y = -3250t + 25000
