Transcript y-intercept

Section 2.4
Using Linear Models
Objective: to write and solve
linear equations which model
a real-world situations.
Using slope and the y-intercept to
write an equation representing a
real-life situation.
 Slope – the rate at which a situation changes is used to
represent the slope.
 Rate of change= change in dependent variable
change in independent variable
 y-intercept – the value at which a situation or
occurrence starts or begins represents the y-intercept.
Write an equation for the following situation,
then use the equation to solve.
1. Jacksonville, FL has an elevation of 12 feet above sea
level. A hot-air balloon taking off from Jacksonville rises
at the rate of 50 feet/minute. Write an equation to model
the balloon’s elevation above sea level (y) as a function
of time (x). Use this equation to find the balloon’s height
after 25 minutes.
Write an equation for the following situation,
then use the equation to solve.
2. An airplane descends at the rate of 300 feet/minute
from an elevation of 5100 feet. Write an equation to
model the airplane’s elevation (y) as a function of time
(x). Use this equation to find the amount of time it takes
the airplane to touch-down on the ground.
Using 2 points to write an equation
representing a real-life situation.
Use the 2 points to find the slope (rate at
which the situation changes).
Use the slope and either of the 2 points to
write an equation using the point-slope
form of an equation.
y – y1 = m(x – x1)
Write an equation for the following situation,
then use the equation to solve.
3.
A candle is 6 inches tall after burning for 1 hour. After 3 hours, the
candle is 5 inches tall Write an equation to model the candle’s height
(y) as a function of time (x). Use this equation to find the candle’s
height after 8 hours.
y = -1/4t + 25/4
a.
What does the slope in question 3 represent?
b.
What does the y-intercept represent?
c.
When will the candle be 4 in tall?
d.
How tall will the candle be after burning for 11 hours?
e.
When will the candle burn out?
Write an equation for the following situation,
then use the equation to solve.
4. The enrollment of the senior class at Seneca Valley in 1995 was 500
students and the senior class enrollment in 2000 was 625 students.
Write an equation to model the senior class enrollment (y) as a
function of the year (x). Let x = 0 represent the year 1990. According
this model, what is the expected senior class enrollment in the year
2010?
Solve: Given a slope and a
point (other than the y-intercept or “starting point”)
5. Between 1990 and 2000, the monthly rent for a one bedroom
apartment increased by $40 per year. In 1997, the rent was $475
per month. Find an equation that gives the monthly rent in
dollars, y, in terms of the year. Let t =0 correspond to 1990.
A candle is 8 inches tall and burns at a rate of 2 inches
per hour. Identify the graph that models the height after
x hours.
y  2x  8
y  8x  2
y
y
10
10
0
Height
(in.)
10 x
y  8x  2
0
[D]
x
y  – 2x  8
y
y
10
10
0
Number 10
of hours
Height (in.)
Nu mber of Hou rs
[C]
[B]
Height (in.)
Nu mber of Hou rs
[A]
Height
(in.)
10 x
0
Number 10
of hours
x
Assignment
 Worksheet #2-4