6.5

Point – Slope Form

Quick Review1. 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:

6.5 – Point – Slope Form

• Basically, when you are given a point and a slope, you can define the line by using the Point-Slope Form.

y – y1 = m(x – x1)

• Where m = slope and (x1, y1) is the given point.

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

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

11 xxmyy