Warm Up

1) Graph the line y = -3

2) You drive 60 miles in 2 hours and 150 miles in 5 hours. What is the rate of change and what does it represent?

Point – Slope Form

y – y1 = m(x - x1)

y – coordinate x – coordinate

Example: y – 6 = 3(x – 5)

Goes through point (5, 6) and has slope of 3

SLOPE

Point-Slope Form

(x, y)

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

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

11 xxmyy

Graphing Using Point-Slope Form

2. Graph the equation 22

15 xy

Graphing Using Point-Slope Form

3. Graph the equation 23

25 xy

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 the relation?(-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

Example:

Altitude Temp.

8000 197.6

4500 203.9

3000 206.6

2500 207.5

Boiling Point of Water

Is the relationship shown by the data in the table linear? If so, model the data with an equation.

Step 1: Find the rates of change for each ordered pair.

Step 2: Use the slope and a point to write an equation.

Ex Identify the form of each equation. Change into the stated form.

1) y = -½x + 3

2) 2x – 3y = 6

3) y – 1 = - (x + 6)

Standard

Slope-intercept

Slope-intercept &

Standard

SummarySlope - Int.

FormStandard Form Point - Slope Form

y = mx + b Ax + By = C y – y1 = m(x - x1)

x and y are variables

x and y are variables

x and y are variables

m = slopeb = y-int.

A, B and C are WHOLE Integers

(x1 y1) is a point of the equation or

graph

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

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

11 xxmyy