Algebra Homework: Equations in Slope-Intercept, Point-Slope, Standard

This assignment focuses on different forms of linear equations, including slope-intercept, point-slope, and standard forms. The assignment begins by identifying the form of given equations and extracting key components like slope, y-intercept, and points. Part II involves writing equations in each form based on real-world scenarios, such as modeling bacterial growth, puppy weight, and costs associated with renting a car and shopping cart expenses. The solutions demonstrate how to identify the slope, y-intercept, and points from the equations, providing a comprehensive understanding of linear equation forms and their practical applications.

1. Which equation from the three scenarios is in slope-intercept form?
Answer:
The slope-intercept form of an equation of line is:y = mx + b.
Comparing the three equations given with the standard slope-intercept form,
the equation
y = 1.8x + 4
is the correct choice.
Identify each of the following from the equation:m = b =
We have,
y = mx + b' y = 1.8x + 4
Therefore,
m = 1.8 b = 4
2. Which equation from the three scenarios is in point-slope form?
Answer:
The point-slope form of an equation of line is:y − y1 = m(x − x1).
Comparing the three equations given with the standard point-slope form,
the equation
y − 96 = 18(x − 5)
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is the correct choice.
Identify each of the following from the equation:m = x1 = y1 =
We have,
y − y1 = m(x − x1) ' y − 96 = 18(x − 5)
Therefore,
m = 18 x1 = 5 y1 = 96
3. Which equation from the three scenarios is in standard form?
Answer:
The standard form of an equation of line is:Ax + By = C.
Comparing the three equations given with the standard form, the equation
4x + y = 40
is the correct choice.
Identify each of the following from the equation:A = B = C =
We have,
Ax + By = C ' 4x + y = 40
Therefore,
A = 4 B = 1 C = 40
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).
At 1 pm in the afternoon temperature (y) in a room was 30◦ Celsius.The
temperature of the room starts to decrease linearly at a rate of 1◦ per hour.
The temperature in the room at some xth hour in the evening is then given
by
y − 30 = −1(x − 1)
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Since the equation is in point-intercept form, we have
y − y1 = m(x − x1) ' y − 30 = −1(x − 1)
Implies, slope:m = −1 and point (x1, y1) = (1, 30).
Notice, the slope here is negative since the temperature is decreasing.
2. Write your own equation in slope intercept form.Identify the slope,
m, and y-intercept, b.
A car rental company charges you a fixed price of10$ for renting a car
and a additionalvariable cost of 0.25$ per mile of usage.The totalbilling
for x miles driven is then
y = 0.25x + 10
Since the equation is in slope-intercept form, we have
y = mx + b' y = 0.25x + 10
Implies, the slope:m = 0.25 and intercept:b = 10.
3. Write your own equation in standard form.Identify the values ofA,
B and C
A shopping cart contains 10 boxes ofcerealand 2 cartons ofmilk. If a
box of cereal costs x dollars and if the total bill was 25$,then the price of
a milk carton (y) is obtained using the relation
10x + 2y = 25
Since the equation is in the standard form, we have
Ax + By = C ' 10x + 2y = 25
Implies,
A = 10 B = 2 C = 25
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