Assignment: Different Forms of Equations
Part I: Read each description of real-world situations represented by equations of lines. Then use
the equations to answer the questions.
A research scientist is
studying how fast a certain
type of bacteria grows. She
measures the number of
bacteria present in a Petri dish
each hour for several hours.
After analyzing the results, she
notices that the number of
bacteria grows at a steady rate
following a linear pattern of
growth. The scientist writes
the equation of the line below
to model the growth of the
bacteria, where y represents
the number of bacteria present
after x hours.
A veterinarian decides to
carefully track a Labrador
Retriever puppy’s growth.
After analyzing the puppy’s
weight over several weeks, the
veterinarian notices that the
puppy’s weight follows a linear
pattern of growth between the
th
th
5 and 25 weeks of growth.
The following equation
represents the approximate
weight of the puppy
throughout this growth period,
where y represents the
puppy’s weight in pounds after
x weeks.
y – 96 = 18(x – 5)
y = 1.8x + 4
Molly has a jar full of quarters
she uses to do laundry at the
laundromat near her
apartment. She uses about the
same number of quarters
every week. To figure out how
long the quarters will last her,
she writes the equation of a
line below, where y represents
the number of quarters in the
jar after x months.
4x + y = 40
1. Which equation from the three scenarios is in slope-intercept form? Scenario 2
Identify each of the following from the equation: m = 1.8
b= 4
2. Which equation from the three scenarios is in point-slope form? Scenario 1
Identify each of the following from the equation:
m=
x1 =
18
y1 =
3. Which equation from the three scenarios is in standard form? Scenario 3
Identify each of the following from the equation:
A=
B=
10
40
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C=
Part II: Now it’s time for you to write your own equations of lines in different forms.
1. Write your own equation in point slope form. Identify the slope, m, and point (x1, y1).
2. Write your own equation in slope intercept form. Identify the slope, m, and y-intercept, b.
3. Write your own equation in standard form. Identify the values of A, B and C.
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