Download 5-4 Point-Slope Form and 5-4 Horizontal and Vertical Lines

Ch 5 Guided Notes.notebook
5­4 Point­Slope Form
November 11, 2016
Where does it come from?
1) Write down formula for slope
2) Cross multiply
3) Erase the little twos
What is it?
Slope
(fill in)
(x1,y1) - ANY point on line
(fill in)
Write the equation of the line that passes through (­2,5) and (1,­6). Put your answer in slope­intercept form. Write the equation in point­slope form of the line that passes through (2,3) and has a slope of ­5.
*Given point and slope ... so use point slope
1) If we use point-slope or slope -intercept
we still need to know the slope. So find the
slope first.
Slope =
2) Now we know the slope and you have a
point (2 in fact). Therefor we should use
point-slope form.
Slope
(fill in)
Slope
(fill in)
(x1,y1) - ANY point on line
(fill in)
Write the equation of the line that passes through (­2,5) and (1,­6). Put your answer in slope­intercept form. Could we do the same thing by graphing
the line and looking at the graph? Yes.
y
6
5
4
3
(x1,y1) - ANY point on line
(fill in)
3) Be sure to check how it wants your answer to be
written by reading the directions. We could then
answer with:
point-slope
or
slope-intercept
(distribute slope and
add/sub the number by y)
Graph the equation 1) Is the equation in point-slope or slopeintercept?
2) So I know
_____________
(remember x and y are opposite for pointslope form)
3) Use the info to draw the graph.
y
6
5
4
3
2
1
x
2
­6
1
­6
­5
­4
­3
­2
­1
0
­1
x
1
2
3
4
5
6
­5
­4
­3
­2
­1
0
­1
1
2
3
4
5
6
­2
­3
­2
­4
­3
­5
­4
­6
­5
­6
1
Ch 5 Guided Notes.notebook
November 11, 2016
5 ­4 Equations of Horizontal/Vertical Lines
Horizontal Lines - All points have the same y-value
Vertical Lines - All points have the same x-value
y
6
y
6
(­5 , 5)
(­2 , 5)
(1 ,
5)
5
(3 ,
5)
4
4
3
3
1
1
­4
­3
­2
­1
x
x
­6
­5
(5 ,
2)
2
2
­6
(5 ,
6)
5
(6 ,
5)
0
­1
1
2
3
4
5
­5
­4
­3
­2
­1
6
0
­1
1
2
3
4
­2
­2
5
6
(5 ,
­2)
­3
­3
(5 ,
­4)
­4
­4
­5
­5
­6
­6
Can we write a horizontal line in slope­intercpet form?
Can we write a vertical line in slope­intercpet form?
Can we write a horizontal line in point­slope form?
Can we write a vertical line in point­slope form?
The equation of every horizontal line is:
The equation of every vertical line is:
Summary:
Vertical Lines
x = the x­intercept
What is the equation of the following line?
Horizontal Lines
y = the y­intercept
y
6
5
4
3
y
6
5
5
4
4
3
­4
­3
­2
­1
0
­1
­5
­4
­3
­2
­1
1
2
3
4
5
6
­6
­5
­4
­3
­2
­1
0
­1
­2
­2
­3
­3
­4
­4
­5
­5
­6
­6
1
2
3
4
5
­1
6
5
5
4
4
0
­1
6
y
6
3
2
1
­2
5
What is the equation of the following line?
2
­3
4
­6
3
­4
3
­5
6
y
­5
2
­4
x
What is the equation of the following line?
­6
1
­3
1
x
x
0
­1
­2
2
1
­5
1
­6
3
2
­6
2
y
6
1
x
1
2
3
4
5
6
­6
­5
­4
­3
­2
­1
0
­1
­2
­2
­3
­3
­4
­4
­5
­5
­6
­6
x
1
2
3
4
5
6
2