Transcript 2.2 Linear Equation

2.2 Linear Equation
Identify linear equations and functions.
Write Linear equations in standard form
Definition of a Linear equation
No variable with an exponent other then 1.
The only operation are addition, subtract and
multiplication of a variable and a number.
4x + 3y = 15 or y = ½x or 7x = 9a - 24
Linear function
A function whose ordered pairs satisfy a
linear equation.
Can be written as
y = mx + b, where m is the slope
or
f(x) = mx + b
Standard form Ax + By = C
A, B and C are not fractions
A and B are not both zero
A is always Positive
6x – 3y = 18
Any y = mx + b can be
written in Standard form
y = -2x + 12
2x + y = 12
y = 4x – 14
-4x + y = - 14
4x – y = 14
add 2x to both sides
subtract 4x to both sides
then multiply both sides by – 1
What about y = ⅔x + 2
Multiply both sides by 3 to get rid of the fraction.
3y = 2x + 6
subtract 2x from both sides
-2x + 3y = 6
Multiply by – 1
2x – 3y = - 6
No fractions, x and y are on the same side, A > 0.
What is Standard form good
for?
Finding the X or Y intercept is easier to
find with Standard form.
Find the x intercept of 4x + 5y = 20
If a point is on the x axis,
then what is its y value?
What is Standard form good
for?
Finding the X or Y intercept is easier to
find with Standard form.
Find the x intercept of 4x + 5y = 20
If a point is on the x axis,
then what is its y value?
y=0
What is Standard form good
for?
Finding the X or Y intercept is easier to find
with Standard form.
Find the x intercept of 4x + 5y = 20
So 4x + 5(0) = 20
4x = 20
x=5
So the point would be (5,0)
Finding the y intercept of 4x + 5y = 20
Last time we let y = 0,
what shall we do this time.
Finding the y intercept of 4x + 5y = 20
Last time we let y = 0,
what shall we do this time.
Let x = 0
4(0) + 5y = 20
5y = 20
y = 4 So the intercept is (0, 4)
Is there another name for the y intercept?
Lets graph an equation using
the intercepts
6x – 2y = 18
x intercept 6x – 2(0) = 18
(3,0)
x=3
Y intercept 6(0) – 2y = 18
(0, - 9)
y = -9
Lets graph an equation using
the intercepts
6x – 2y = 18
x intercept 6x – 2(0) = 18
x=3
Y intercept 6(0) – 2y = 18
y = -9 (0, - 9)
3
-9
(3,0)
Homework
Page 66 – 67
# 15 – 23 odd, 27 – 35 odd, 39 – 47 odd,
53 – 55, 64 – 76 even