Notes – Characteristics & Applications of Linear Functions
CCGPS Coordinate Algebra
Notes __________________________
Date________________
Vocabulary
-intercept (also known as “_____________”):
On the graph the point where the given line meets the x-axis (_____________________ axis)
Algebraicallywhere the value of y is _________________
In real world applicationsthe __________________ value
-intercept:
On the graphthe point where the given line meets the y-axis (______________________ axis)
Algebraicallywhere the value of _____ is zero
In real world applicationsthe ___________________ value
Rate of Change:
On the graphslope
Algebraicallyslope,
; how _______________ the line is
,
In real world applications how quickly something increases
or ___________________
Interval of Increase: the part of a graph that has a ______________________ slope
Interval of Decrease: the part of a graph that has a ______________________ slope
Real World Applications
Example 1:
Crystal is trying to determine how much money she will have by the end of this year to buy Christmas
presents for her family. She makes 12 dollars an hour at work and gets a 100 dollar Christmas bonus. If
she works 1,040 hours this year, how much Christmas money will she have?
Example 2:
Scotty bought a large bag of potato chips on Monday. There are 125 chips in the bag. If he eats 15 chips
everyday, on what day will he finish the bag of chips?
Finding Zeros of a Linear Function
Given a linear function, substitute (_________________) zero for .
Why??? Because the value of on the x-axis is ZERO!
Remember, if we are standing on the -axis how many units have we moved vertically?
None, so
.
Determining Whether a Given Value is a Zero
Given a linear function and a value, to determine whether that value is a zero of the function:
1. Substitute ___________________________________________ for in the given function.
2. Then solve for .
If
If
, then the given value IS a zero.
is NOT ZERO, then the given value is _________ a zero.
Example 1:
Find the zero of the linear function
.
Example 2:
You can run a 100 meter race at an average rate of 4.8 meters per second. The distance, , you have left
to run after seconds is given by the function
. Find the zero of the function to the
nearest tenth. Explain what the zero means in this situation.
Example 3:
Determine whether six is a zero of the function
.