Dynamics of Algebra 2
Name:
Date:
Block:
Solutions
2.3 Application Examples
1. The equation
50 5 represents your elevation y in feet for each minute x you hike from a trailhead.
a. Define your variables.
x:_________________________________
y: _________________________________
b. Write this equation in slope intercept form.
c. Graph the equation of the line to model the situation.
d. What does the slope mean in the context of the problem? Are
you hiking up or down the mountain?
e. What does the y-intercept mean in the context of the problem?
(we set ________ )
f.
What does the x-intercept mean in the context of the problem?
(we set ________ )
g. In the given problem, what does the point (2,70) represent?
h. According to this model, what elevation are you at after 8
minutes? (use your graph and the equation. Label the point with
on your graph.)
i.
According to this model, how long have you been walking if you
are at 20 ft? (use your graph and the equation. Label the point
with on your graph.)
2. The equation
2
30 models the number of pages y you have left to read after reading for x
minutes.
a. Define your variables.
x:_________________________________
y: _________________________________
b. Write this equation in slope intercept form.
c. Graph the equation of the line to model the situation.
d. What does the slope mean in the context of the
problem?
e. What does the y-intercept mean in the context of the
problem?
f.
What does the x-intercept mean in the context of the
problem?
g. In the given problem, what does the point (5,20)
represent?
h. According to this model, what page are you on after 10 minutes? (use your graph and the
equation. Label the point with
i.
on your graph.)
According to this model, how long have you been reading if you are on page 24? (use your graph
and the equation. Label the point with on your graph.)
3. The equation 7
3
42 models the way you can score 42 points in a football game. For every field
goal y you score 3 points and for every touchdown x you score 7 points.
a. Define your variables.
x:_________________________________
y: _________________________________
b. Write this equation in slope intercept form.
c. Graph the equation of the line to model the situation.
d. What does the slope mean in the context of the problem?
e. What does the y-intercept mean in the context of the problem?
f.
What does the x-intercept mean in the context of the problem?
g. In the given problem, what does the point (3,7) represent?
4. A cab company charges a $3 boarding rate in addition to its meter, which is $2 for every mile.
a. Define your variables.
x:_________________________________
y: _________________________________
b. Write this equation in slope intercept form.
c. Graph the equation of the line to model the situation.
d. What does the slope mean in the context of the problem?
e. What does the y-intercept mean in the context of the problem?
f.
What does the x-intercept mean in the context of the problem?
g. In the given problem, what does the point (2, 7) represent?
h. According to this model, how long have you been riding in the cab if your fair is $13? (use your
graph and the equation. Label the point with
on your graph.)
5. A bus company charges a $4 boarding rate in addition to its meter which is $0.75 (or ¾) for every mile.
a. Define your variables.
x:_________________________________
y: _________________________________
b. What is the equation of the line that represents
this bus company's rate?
c. Graph the equation of the line to model the
situation.
d. What does the slope mean in the context of the
problem?
e. What does the y-intercept mean in the context of
the problem?
f.
What does the x-intercept mean in the context of the problem?
g. In the given problem, what does the point (4, 7) represent?
h. According to this model, how long have you been riding in the cab if your fair is $13? (use your
graph and the equation. Label the point with
i.
on your graph.)
According to this model, how much money is a 9 mile cab ride? (use your graph and the equation.
Label the point with on your graph.)
6. A taxi company does not charge a boarding fee but then has a meter of $4 an hour.
a. Define your variables.
x:_________________________________
y: _________________________________
b. What is the equation of the line that represents this taxi
company's rate?
c. Graph the equation of the line to model the situation.
d. What does the slope mean in the context of the problem?
e. What does the y-intercept mean in the context of the problem?
f.
What does the x-intercept mean in the context of the problem?
g. In the given problem, what does the point (3, 12) represent?
7. Limo service charges a $15 boarding rate, no matter what the mileage is on the meter. What equation
represents this limo service company's rate?
a. Define your variables.
x:_________________________________
y: _________________________________
b. What is the equation of the line that represents this taxi
company's rate?
c. Graph the equation of the line to model the situation.
d. What does the slope mean in the context of the problem?
e. What does the y-intercept mean in the context of the problem?
f.
What does the x-intercept mean in the context of the problem?
g. In the given problem, what does the point (1, 15) represent?