GOAL: Create equations of lines using Point Slope Form (P.S.F.) and
convert it into Slope Intercept Form (S.I.F)
Recall:
Slope intercept form:
There is another form of a line called Point Slope Form (P.S.F.)
 Where the is the slope
 And
is any point on the line
 and are variables
P.S.F. has the advantage of being able to write the equation quickly and
easily because you’re not going through the work to find “ ”.
EX: Find the equation of the line in P.S.F. passing through the given
points.
1) A(2,1) and B(5,-6)
We still the slope
for either form…
Now we can write the formula using either (2,1) (in other
words
)
or using (5,-6)
Both are valid!
2) C(4,-3) and D(-9,-1)
We still the slope
for either form…
Now we can write the formula using either (4,-3) (in other
words
)
or using (-9,-1)
Both are valid!
EX: Write the equation of the line in P.S.F. with slope
and
passing through (6,-8)
We already have the slope, and the point. That’s all we need for P.S.F.
To convert from Point Slope Form (P.S.F.) to Slope Intercept Form
(S.I.F.)
a. Distribute the slope
b. Isolate the
EX: Convert the following equations of a line from P.S.F. to S.I.F. and
then state the y-intercept.
1)
The y-intercept is (0,22)
2)
The y-intercept is (0,-8.5)
3)
The y-intercept is (0,79.54)
EX: Create the equation of the line which passes through the points
A(2.1, 1.9) and B(-2.8, 3.5) in P.S.F. Then convert it into S.I.F.
P.S.F. Using (2.1, 1.9)
S.I.F.:
EX: Consider Data Set 5
5. Calcu-Chem
Calcu-Chem produces a drug, which eliminates migraine headaches.
The following table provides guidelines for dosage, and maximum
dosage (measured in milligrams) for a patient’s weight (measured in
pounds).
Patient
ID
A
B
C
D
E
F
G
H
I
J
K
L
Weight (lbs)
88
99
110
121
132
143
154
165
176
187
198
209
Suggested Dose
(mg)
40
45
50
55
60
65
70
75
80
85
90
95
Maximum Dose
Allowed (mg)
66
75
83
91
100
108
116
125
133
141
150
158
Create an equation of a fit line in P.S.F. using Patient A and Patient F
(suggested dose). Then convert it into S.I.F. and verify the y-intercept
by looking at the graph.
Our points are (88,40) and (143,65)
P.S.F. Using (88,40)
Converting to S.I.F.
The y-intercept seems to be zero. Look at the graph again
?!?!?
You might say “Hey! The y-intercept looks to be closer to 20!”
But are you really looking at the y-axis? Notice the graph starts at
. If the graph “extended” to the left far enough you could see
it probably would hit the y-axis at the origin.
Here is a version of the graph
with the axis extended a bit.