Home Work 3
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School
Community College of Aurora *
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Course
1340
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
7
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#3 Homework 4.1 (part 2) Equations of lines and 4.2 Modeling with
Linear Functions
Daler Nizomaddinov
Question 1
1/1 pt
84
Question 2
1/1 pt
1-2
95
Question 3
1/1 pt
2
97
Question 4
1/1 pt
0-2
72
Consider the line that contains the points and .
Write the equation for the line in slope-intercept form .
y
=
4
3
x
−
2
3
Write the equation for the line in point-slope form .
y
+ 0 =
4
3
x
− 2
(
)
Write the equations of a line through the point (2,1) with a slope of in:
Point Slope: y
− 1 = −2
x
− 2
Slope-intercept: y
= −2
x
+ 5
Standard: 2
x
+
y
= 5
(
)
Find the equation of the line through the points and in slope intercept form
y
= −8
x
+ 1
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Question 5
1/1 pt
1-2
97
Write the slope-intercept form of the line through the point (-5,3) and parallel to the line y= 2/5 x+1
y
=
5
2
x
+ 5
Graph the system of equations: 1
2
3
4
5
6
7
8
9
10 11 12
-1
-2
-3
-4
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Question 6
0.5/1 pt
0-2
98
Write the slope-intercept form of the line through the point (2,-1) and parallel to the line y= -5/4 x+2
y
= −
4
5
x
+
2
3
Graph the system of equations: 1
2
3
4
5
6
7
8
9
10 11 12
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
1
2
3
4
5
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9
10
11
12
-1
-2
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-4
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-11
-12
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Question 7
1/1 pt
0-1
99
Question 8
1/1 pt
2
98
Write the slope-intercept form of the line through the point (2,-1) and perpendicular to the line y= 4/5
x+2
y
= −
4
5
x
+
2
3
Graph the system of equations: 1
2
3
4
5
6
7
8
9
10 11 12
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
1
2
3
4
5
6
7
8
9
10
11
12
-1
-2
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A phone company charges for service according to the formula: , where is the
number of minutes talked, and is the monthly charge, in dollars.
The rate of change in this equation is: 0.04
The initial value in this equation is: 11
Question Help: Dollars per Minute
Dollars
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Question 9
1/1 pt
1-2
99
Question 10
1/1 pt
1
99
A town's population has been growing linearly. In 2003 the population was 35,000. The population has
been growing by 700 people each year.
Write an equation for the population, P, years after 2003.
P = 700
·
x
+ 35000
Use the formula to find the population in 2009: 700
·
6 + 35000
Question Help: Video
In 2001, a school population was 1542. By 2008 the population had grown to 1990.
1) How much did the population grow between the year 2001 and 2008?
448
students
2) How long did it take the population to grow from 1542 students to 1990 students?
7
years
3) What is the average population growth per year?
64
4) What was the population in the year 2000?
1478
students
5) Find an equation for the population, , of the school years after 2000.
= 64
t
+ 1478
6) Using your equation, predict the population of the school in 2011.
2182
students
Question Help: students/year
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Question 11
1/1 pt
2
98
Question 12
1/1 pt
2
98
A city's population in the year 1973 was 3,501,800. In 1955 the population was 3,492,800.
Compute the slope of the population growth (or decline) and choose the most accurate statement from
the following:
The population is decreasing at a rate of 400 people per year.
The population is decreasing at a rate of 500 people per year.
The population is increasing at a rate of 400 people per year.
The population is increasing at a rate of 500 people per year.
The population is increasing at a rate of 550 people per year.
The population is decreasing at a rate of 550 people per year.
Question Help: Video
The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and
then a certain amount of money per minute used on the phone. If a customer uses 370 minutes, the
monthly cost will be $131.5. If the customer uses 820 minutes, the monthly cost will be $244.
A) Find an equation in the form where is the number of monthly minutes used and is
the total monthly of the Ringular plan.
Answer: 0.25
x
+ 39
Do not use any commas in your answer.
B) Use your equation to find the total monthly cost if 804 minutes are used.
Answer: If 804 minutes are used, the total cost will be 240
dollars.
Question Help: Video
In 1993, the moose population in a park was measured to be 3220. By 1998, the population was
measured again to be 4270. If the population continues to change linearly:
A.) Find a formula for the moose population, , in terms of , the years since 1990.
210
t
+ 2590
B.) What does your model predict the moose population to be in 2007?
6160
Question Help: Video
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