Today’s Topics:
• Identify Linear Functions
• Intercepts/Slopes
• Graph Linear Functions
• Rate of Change
• Identity and Constant Functions
• Apply Linear Revenue, Cost, and Profit
• A function whose graph is a line is a _____________.
Linear Function
A linear function is a function that can be written in the form
𝑓 𝑥 = ________________, 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 = ______and solve for _____
To Find the x-intercept:
Let y = ______ and solve for ______
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 = ____________________________
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. (
,
) and (
,
)
B. (
,
) and (
,
)
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 =
Where,
P(x) =
R(x) =
C(x) =
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