Download Unit 1-5 Linear Functions

Today’s Topics:
• Identify Linear Functions
• Intercepts/Slopes
• Graph Linear Functions
• Rate of Change
• Identity and Constant Functions
• Apply Linear Revenue, Cost, and Profit
• Solving Linear Equations
• Solve Real-World Application
• Solve Literal Equations
• A function whose graph is a line is a linear functions.
Linear Function
A linear function is a function that can be written in the form
𝑓 𝑥 = 𝑎𝑥 + 𝑏, where a and b are constants.
Ex) Linear:
y= -17.8x – 6
y=4
Non-Linear:
𝑦 2 + 4𝑥 − 3
y = 𝑥2
Intercepts are points that cross the x-axis and the y-axis.
To Find the y-intercept:
Let x = 0 and solve for y
To Find the x-intercept:
Let y = 0 and solve for x
Example:
Find the x-intercept and y-intercept of the graph 4x-12y =22
A student promised to pay off a $35,000 loan plus the $7,000 interest
on this loan by making 120 monthly payments of $350. Although the
amount of money remaining to be paid changes every month, it can be
modeled by the linear functions
𝑦 = 42000 − 350𝑥
where x is the number of monthly payments made.
a. Find the x-intercepts and the y-intercepts of the graph of this liner
equation.
b. Interpret the intercepts in the context of this problem situation.
c. How should x and y be limited in this model so that they make sense
in the application?
d. Use the intercepts and the results of part (c) to sketch the graph of
the given equation.
Slope =
𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐶ℎ𝑎𝑛𝑔𝑒
𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐶ℎ𝑎𝑛𝑔𝑒
=
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
Find the slope of each:
A. (-3, 2) and (5, -4)
B. (8, -3) and (7, -4)
Match each equation with the possible slope:
A. y = 2x + 3
B. y = 5
C. x = 2
D. y = - 2x + 5
The slope of the graph of the equation 𝑦 = 𝑚𝑥 + 𝑏 is m and the
y-intercept of the graph b, so the graph crosses the y-axis at
(0,b).
Constant Function
y = b, where b is a real number
Identity Function
y=x
The profit that a company makes on its product is the difference
between the amount received from sales (revenue) and the
production and sales cost.
Goes a little something like this in the math world:
𝑃 𝑥 = 𝑅 𝑥 − 𝐶(𝑥)
Where,
P(x) = profit from sale of x units
R(x) = total revenue from sale of x units
C(x) = total cost of production and sale of x units
Apple manufactures a 16GB Wi-Fi-only iPad 3 and sells them for
$499. The cost incurred in the production and sale of the iPad are
$500,000* plus $316** for each iPad produced and sold. Write
the profit function for the production and sale of x iPads.
*Yeah….I made this up.
** According to http://www.ijailbreak.com/ipad/how-much-does-new-ipad-cost-to-make
𝐴. If 2𝑥 + 5 = 7, then x =?
B. What is the value of x if −5 +
𝑥
3
= −4?

• Solve:
Simplify
o Get rid of parenthesis.
5𝑥
3𝑥 1
−1=
+
4
4 2


Multiply ALL terms by
the lowest common
denominator.
Continue Simplifying
o Combine like terms on
either side of the equal
sign.
• Solve:
𝑥 2 2𝑥 4 1
+ =
− +
2 5
3 5 2


If there is more than
one x left, get rid of
one of them.
Follow SADMEP
It is hard for some people to pay off credit card debt in a
reasonable period of time because of high interest rates. The
interest paid on a $10,000 debt over 3 years is approximated
by 𝑦 = 175.393𝑥 − 116.287 dollars when the interest rate is
x%. What is the interest rate if the interest is $1637.60?
For the function 𝑓 𝑥 = 22𝑥 − 264
• The zero of 𝑓 𝑥 = 22𝑥 − 264
• The x-intercept of the graph y= 22𝑥 − 264
• The solution to the equation 22x - 264 = 0
Simple Interest:
The formula for the future value of an investment of P dollars at
simple interest rate r for t years is 𝐴 = 𝑃(1 + 𝑟𝑡). Solve the
formula for t, the years.
To find the Surface Area of a cylinder is given by
S𝐴 = 2𝜋𝑟 2 + 2𝜋𝑟ℎ, where r is the radius and h is the height.
Solve the formula for h, the height.
4.3 Due Thursday
Quiz Friday In-Class
1.3/2.1(todays) Due Next Tuesday