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

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

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

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

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)

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 = - 2 y = 4x – 14

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.

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 1998. 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 = 2.80 – 2.38 = 0.42 1 – 0

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 + 2.38

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

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) 1 2 3 4 5 Year (0  1998)

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

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

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

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

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