Today, you will learn to:
Determine if a set of ordered pairs is a linear function
Write a linear function in Standard Form
Determine if an equation represents a linear function
Graph linear functions using intercepts
3.1
Linear Functions
Is it a linear function?
x
y
1
-5
2
-3
3
-1
4
1
5
3
x
y
5
1
4
4
3
9
2
16
1
25
You can tell if a function is linear by looking at its equation.
If you can write the equation in standard form,
then the function is linear.
The standard form for a linear equation is
Ax + By = C
Where A > 0,
A &B are both not zero, and
A, B, & C are integers with a greatest common factor of 1.
Is it a linear function?
If so, write the equation in standard form and
give the values of A, B, and C.
3x - 2y = -9
6x2 - y = 8
|x| +3 = y
x+
6
y
= 12
y =
1
2
x - 43
7xy + 2 = -18
5y = -10
Find the intercepts of 2x + 3y = 18
Then graph the function.
Find the intercepts of 4x - 5y = 40
Then graph the function.
Find the intercepts of this function
x
y
-1
0
2
5
10
12
-8.8
-8
-6.4
-1.6
0
1.6
The population of Historytown is 1500 students.
Each week, 100 students leave Historytown and move to
Algebratown.
Write a function rule for the population of Historytown after
x weeks.
Graph your function and find the intercepts.
Explain, specifically, what the x-intercept represents.
Explain, specifically, what the y-intercept represents.
Student Council is selling donuts and hot chocolate.
Donuts are $1 each and hot chocolate is $0.50 per cup.
They want to make $ 200.
Write an equation for this situation. Then graph it.
Describe exactly what the intercepts represent.