Chapter 3B Flashcards
What form is this called?
y+mx+b
Slop-intercept form
Why is it called slope intercept form?
Because the slope and the Y intercept can be read directly from the equation.
The ‘b’ and the Y equal in
y= mx+b
represents what value on the Cartesian coordinate sytem?
The value of the Y intercept.
Slope intercept form is the most useful of all forms because the information that we can determine_______ at it
simply by looking
The ‘b’ in
y= mx+b
represents the Y intercept because if you set x to 0
then…
then y = b
What are the steps to graph a line by using the slope and y intercept?
Hint: S.I.C.C.
- Write the equation in slope intercept form by solving for Y
- Identify the Y intercept [graph the point (0,b)]
- Identify the slope of the line. Use the geometric interpretation of slope (“rise over run”) to find anther point on the graph by counting from the y-intercept.
- Join the two points with a line to obtain the graph.
When graphing a line whose slope is a fraction, the fraction is already in rise/run form.
The numerator represents _______
and the denominator represents ________
Y value
X value
When graphing a line whose slope is a whole number, the whole number isn’t in rise/run form until it is ________________________.
placed over denominator of one
When graphing a line whose slope is a whole number, the slope can be written in different but equal forms. What are they?
A
_
-B
and
-A
_
B
Both of these are equivalent.
How to write an equation with only a point and the slope.
Plug in the x and y values
Plug in the slope
Solve for b
Write equation in slope intercept form
What form is this?
y-y1 = M(x-x1) [y1 & x1 are given]
y-y1 m= \_\_\_\_
x-x1
[y1 & x1 are given]
Point-Slope-Form
What is the second way to write an equation with only a point and the slope?
By using the Point-Slope-Form formula.
How to use the point slope formula to write an equation with only a point and the slope.
- Plug in the slope
- Plug in the x & y points
- Distribute (carefully)
- Solve and until the final answer in slope intercept form.
How do you write an equation with two points?
- Plug both values into the point slope form.
- Solve for the Slope
- Pick ONE point and plug it into either point slope or slope intercept form.
- Plug in the slope
- Solve and write the final equation in slope intercept form.
In order to write a standard linear equation in two variable where A<0 you simply have to ______
Multiply the each side of the equation by -1
What type of linear equation am I ???
x=k
Vertical line
ex. x=3
What type of linear equation am I ???
Ax+By= C
Standard form
ex. 3x-2y=12
What type of linear equation am I ???
y-y1=m(x-x1)
y-y1 m= \_\_\_\_
x-x1
Point-slope form
ex. y+3=3/2(x-2)
What type of linear equation am I ???
y=mx+b
Slope-intercept form
ex.y=3/2x-6
What type of linear equation am I ???
y=k
Horizontal line
ex. y=3
Can a vertical line be written in slope intercept form?
No because vertical lines have NO SLOPE
In an ordered pair the x & y are known as…
The components.
Any set of ordered pairs is called a…
Relation
The set of all first components of the ordered pairs is called..
A domain of the relation
The set of all second components of the ordered pairs is called..
The range of relation.
In the following relation what is the Domain?
…what is the Range?
(3,5),(3,6),(3,7),(3,8)
Domain (3)
Range(5,6,7,8)
A set of ordered pairs in which each first component corresponds to exactly one second component.
Basically if the the first number appears more than once in a set of ordered pairs it is a Non-Function.
A function.
Which two of the following three relations is a function?
Why?
(3,5),(3,6),(3,7),(3,8)
(9,5),(6,6),(2,7),(1,8)
(5,3),(6,3),(7,3),(8,3)
(9,5),(6,6),(2,7),(1,8)
&
(5,3),(6,3),(7,3),(8,3)
Because the first component (Domain Element ) corresponds to only one second component (range element).
