Name: _______________________________________________
Algebra 1
Writing Linear Functions Word Problems by Finding Slope and y-intercept
Word Problem Examples of slope
f(x) = mx + b
Average rate of change
Slope always the coefficient in f(x) = mx + b
SLOPE
Word Problem Examples of y-intercept
f(x) = mx + b
x-coordinate is always 0  (0, y-int)
Always the constant in f(x) = mx + b
Y-INTERCEPT
Y unit per X unit
Starting value
Y unit for each X unit
Initial value
Y unit for every X unit
One-time value
$10 per hour he earns at work
$20 initial fee to register for classes at library
8 millimeters each second a particle moved
during a laboratory experiment
$15 entrance fee for school play
50 km every hour that a car is traveling
50 feet starting height for an object falling to
the ground.
1. In 1996, the enrollment in West Lake High School was approximately 1400 students. It is predicted that in
the future, the enrollment will increase by an average of 30 students per year.
a) Write a linear function E(t) that models the school’s enrollment, E, in terms of the number of years since
1996, t.
b) What is the slope?
Explain what it represents in this problem.
c) What is the y-intercept?
Explain what it represents in this problem.
d) Use your function to estimate the school’s enrollment in the year 2002.
2. Between 2005 and 2015, the population of a city decreased by about 150 people per year. In 2008, the
population was 38,450 people.
a) Write the linear equation P(t) for the population P of the city as a function of years t, where t is the number
of years since 2005.
b) What is the slope?
Explain what it represents in this problem.
d) Label the interval of the domain. Explain.
e) What is the maximum? Explain
c) What is the y-intercept?
Explain what it represents in this problem.
3. In Bicycle Moto Cross (BMX) racing, racers purchase a one year membership to a track. They also pay an
entry fee for each race at that track. One racer paid a total of $125 after 5 races. A second racer paid a total of
$170 after 8 races.
a) Write a linear equation P(r) that models your total amount paid P (in dollars) as a function of the number of
races r.
b) What is the slope? What does the slope represent?
c) What is the y-int? What does the y-int represent?
d) Find r such that P(r) = 200. Explain what this represents in the context of this problem.
4. A photographer charges $35.50 per hour plus a one-time set-up fee. The total cost for 3 hours was $161.50.
When hiring this photographer a customer must sign a contract agreeing to the described terms above and
agreeing the photography session does not exceed 6 hours.
a) Write a linear equation T(h) that represents the total cost T (in dollars) with respect to time h (in hours).
b) What is the slope?
Explain what it represents in this problem.
c) What is the y-intercept?
Explain what it represents in this problem.
d) Find T(4.5). Explain what it represents in this problem.
e.) What is the interval of the domain?
f.) What is the minimum?