1. Lines in the Plane and Slope
Section P.4
(Part 3)

2. Graphing using Point – Slope form
Must be a non-vertical line!
Use this when given a slope and a point.
y – y1 = m(x – x1)
Slope of line
y – coordinate of point
x – coordinate of point

3. Example: Point-Slope Formula
Find the equation of the line through the point (1,-2) with a slope of 3.
Use the Point-Slope Formula:
y - y1 = m(x - x1).
y – (-2) = 3(x - 1) Substitute
y + 2 = 3x – 3 Simplify
y = 3x – 5 Slope-intercept Form

4. Example: Point Slope Form
Find the equation for the line passing through the points (3,-2) and (6,10)
First, calculate the slope, m =
(10 – -2) DY 12 = = 4
m =
(6 – 3) 3 DX

5. Example: Point Slope Form
Find the equation for the line passing through the points (3,-2) and (6,10)
Next plug it into Point Slope Form :
y – y1 = m(x – x1)
Select one point:
Let’s use (3,-2)
The Equation becomes:
y – -2 = 4(x – 3)

6. Example: Point Slope Form
Simplify the equation by putting it into Slope Intercept Form
y + 2 = 4x – 12
Subtract 2 from both sides gives:
y + 2 = 4x – 12
-2 =
y = 4x – 14

7. Lines Used for Estimation
The cash flow per share for Verizon was $2.38 in 1998 and $2.80 in 1999.
Using only this information, write a linear equation that gives the cash flow per share in terms of the year.

8. The slope of the line passing through these points is:
Solution:
The cash flow per share for Verizon was $2.38 in 1998 and $2.80 in 1999.
Let x = 0 represent Then the two given values are represented by the points:
(0, 2.38) and (1, 2.80)
The slope of the line passing through these points is:
m = – 2.38 = 0.42
1 – 0

9. Solution: y = 0.42x + 2.38 We have two points (0, 2.38) and (1, 2.80)
and the slope 0.42
Using the point (0, 2.38), write equation in point slope form:
y – 2.38 = 0.42 (x – 0)
Simplify:
y = 0.42x

10. Making Predictions: y = 0.42x + 2.38
You can use this to predict future cash flows.
For example:
Predict the cash flows in 2000, 2001, and 2002.
Since year x = 0 corresponds to 1998,
2000  x = 2
2001  x = 3
2002  x = 4
If you plug in the values for x in the equation, there is a cash flow of $3.22 in 2000, $3.64 in 2001, and $4.06 in 2002

11. Verizon Cash Flow 5 4 y 3 2 1 y x
Here is the graph corresponding to our linear equation and predicted cash flows.
(4, 4.08)
(2, 3.22)
Cash flow per share (in $)
(1, 2.80)
(3, 3.64)
(0, 2.38)
Year (0  1998)

12. Names for Prediction Methods:
The prediction method in the last example is called linear extrapolation.
These points lie on the outside of the given points. y x
Given points
Estimated point

13. Names for Prediction Methods:y x
Given points
When the estimate point lies between two given points, the method is called linear interpolation.
Estimated point

14. Summary of the Equations of Lines:
Ax + By = C  Standard form
x = a  Vertical Line
y = b  Horizontal Line
y = mx + b  Slope-intercept Form
y – y1 = m(x – x1)  Point-slope form

15. Worksheet: Point-Slope Form and Standard Form (Double Sided)
Classwork:
Worksheet: Point-Slope Form and Standard Form (Double Sided)

16. Homework: Exercises: 41 – 46, 51, 53, 55, 56, 57, 93
Textbook Pg 53 – 55
Exercises:
41 – 46, 51, 53, 55, 56, 57, 93