Solving a system of linear equations using a graph
A system of linear equations includes two or more linear equations. The graphs of two lines will intersect at a single point if they are not parallel. Two parallel lines can also intersect if they are coincident, which means they are the same line and they intersect at every point. For two lines that are not parallel, the single point of intersection will satisfy both equations and therefore represent the solution to the system.
To find this point when the equations are given as functions, we can solve for an input value so that
In other words, we can set the formulas for the lines equal to one another, and solve for the input that satisfies the equation.
Finding a point of intersection algebraically
Find the point of intersection of the lines
and
Set
This tells us the lines intersect when the input is
We can then find the output value of the intersection point by evaluating either function at this input.
If we were asked to find the point of intersection of two distinct parallel lines, should something in the solution process alert us to the fact that there are no solutions?
Yes. After setting the two equations equal to one another, the result would be the contradiction “0 = non-zero real number”.
Look at the graph in
[link] and identify the following for the function
y- intercept
x -intercept(s)
slope
Is
parallel or perpendicular to
(or neither)?
Is
an increasing or decreasing function (or neither)?
Write a transformation description for
from the identity toolkit function
Slope -1
Neither parallel nor perpendicular
Decreasing function
Given the identity function, perform a vertical flip (over the
t -axis) and shift up 5 units.
A company sells sports helmets. The company incurs a one-time fixed cost for $250,000. Each helmet costs $120 to produce, and sells for $140.
Find the cost function,
to produce
helmets, in dollars.
Find the revenue function,
from the sales of
helmets, in dollars.
Find the break-even point, the point of intersection of the two graphs
The cost function in the sum of the fixed cost, $125,000, and the variable cost, $120 per helmet.
The revenue function is the total revenue from the sale of
helmets,
The break-even point is the point of intersection of the graph of the cost and revenue functions. To find the
x -coordinate of the coordinate pair of the point of intersection, set the two equations equal, and solve for
To find
evaluate either the revenue or the cost function at 12,500.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
