5.4 Point-Slope Form of a Linear Equation

Standard: SWBAT derive linear equations by using the point-slope formula and be able to

explain the sequence of steps.

http://antwrp.gsfc.nasa.gov/apod/ap081203.html

A Happy Sky Over Los Angeles superposition of our Moon and the planets Venus and Jupiter

Mini Quiz 43

1. Find the x- and y-intercept of 3x – 4y = 12

2. Graph the line y = -3

3. Write the equation in Standard Form:2

34

xy

Quick Review

1. What is the Slope-Intercept Form?

y = mx + b

2. What is the Standard Form?

Ax + By = C

3. How does an equation of a vertical line look? What is the slope?

x = #, slope = undefined

4. How does an equation of a horizontal line look? What is the slope?

y = #, slope = 0

Overview

Point-Slope Form Graphing Using Point-Slope Form Writing an Equation in Point-Slope Form Writing an Equation Using a Table

Forms we’ve learned so far… Slope-Intercept Form: y = mx + b Standard Form: Ax + By = C

Point-Slope Formy – y1 = m(x – x1)

12

12

xxyy

m

11 xxmyy

11 yyxxm (x, y)

(x1, y1) = (-2, -2)

Derived (came from) the slope formula:

Point-Slope Form

(x, y)

(x1, y1) = (-2, -2)

1. Write the equation in Point-Slope Form of the graph below:

We know the slope is 2/3

23

22 xy

11 xxmyy We know the point (-2, -2), so x1 = -2 and y1 = -2

Plug it into the Point-Slope Form:

Graphing Using Point-Slope Form

2. Graph the equation

What is the ordered pair?

(x1, y1) =

What is the slope?

m =

22

15 xy

(2, 5)

2

1

(2, 5)

2

1

Graphing Using Point-Slope Form

3. Graph the equation

What is the ordered pair?

(x1, y1) =

What is the slope?

m =

23

25 xy

(-2, 5)

3

2

Write an Equation in Point-Slope Form Given a Point and a Slope

4. (-1, -3); Slope = 4

y + 3 = 4(x + 1)

5. (-10, 0); Slope = 2

y = 2(x +10)

6. (-4, 3); Slope = -6

y – 3 = -6(x +4)

11 xxmyy

Steps:

1. Find the slope between the two points.

2. Pick one point to use in order to write the equation.

3. Plug in the slope and coordinate from the point into the Point-Slope Form

Write an Equation in Point-Slope Form Given Two Points

7. (-3, 6) and (1, -2)

y – 6 = -2(x + 3) or y + 2 = -2(x – 1)

8. (-2, 3) and (-1, 1)

y – 3 = -2(x + 2) or y – 1 = -2(x + 1)

9. (-2, -5) and (7, -6)

y + 5 = - (x + 2) or y + 6 = - (x – 7)

Write an Equation in Point-Slope Form Given Two Points

9

1

11 xxmyy

9

1

Writing an Equation from a Table

What is the independent and dependent variable?

x – independent; y – dependent Find the rate of change:

What is the slope?4/10 = 2/5

What is one ordered pair?(-11, -7), (-1, -3), (4, -1), (19, 5)

What is a possible equation in Point-Slope Form?

y + 7 = 2/5 (x + 11)

tindependenin change

dependentin change change of rate

Wrap Up Point-Slope Form Graph Using Point-Slope form

Start at the point Graph the slope

Write equation in point-slope form Given a point and a slope Given two points

Writing an equation from a table Find the rate of change (slope) Pick a point to plug in

HW: P. 255 #1-53 EOO, #67-71 odd

DLUQ: What two things are given to you in the point-slope form?

11 xxmyy